Mensuration

Problem 1

Find the length of line segment $AB$ where $A$ and $B$ are intersections of $2x + 3y = 6$ and $x^2 - 2y^2 - xy = 0$ .

See Solution

Problem 2

Find the dimensions of a rectangle with area $21 \mathrm{yd}^{2}$ and length $1 \mathrm{yd}$ less than twice the width.

See Solution

Problem 3

Find the area between the curves $y=3 x^{2}$ , $y=0$ , and $x=3$ . Choose integration with respect to $x$ or $y$ .

See Solution

Problem 4

已知半径为1的球体，求四棱锥体积最大时的高度选项：A. $\frac{1}{3}$ B. $\frac{1}{2}$ C. $\frac{\sqrt{3}}{3}$ D. $\frac{\sqrt{2}}{2}$

See Solution

Problem 5

Find the apparent distance from the top of a 4.20 cm benzene layer to the bottom of a 6.20 cm water layer at normal incidence.

See Solution

Problem 6

A mud house has a cone roof over a cylinder. Given dimensions, find $A B$ , volume, surface area, and house choice.

See Solution

Problem 7

Find the volume of a cuboid with face areas $35 \mathrm{~cm}^{2}$ , $42 \mathrm{~cm}^{2}$ , and $14 \mathrm{~cm}^{2}$ .

See Solution

Problem 8

Calculate the inductance and capacitance per phase of a 40 km overhead line with copper conductors (1.5 cm diameter) in two spacings: 75 cm flat and triangular sides 70 cm, 90 cm, 110 cm.

See Solution

Problem 9

A rectangle has a length of 4 times its width and an area of 16. Find its perimeter. A. 8 B. 10 C. 20 D. 32

See Solution

Problem 10

Съществува десетоъгълна призма с периметър на основата $30 \mathrm{~cm}$ и околен ръб $8 \mathrm{~cm}$ . Намерете сбора на ръбовете в см.

See Solution

Problem 11

Una finca rectangular de 187 m de largo y 87 m de ancho necesita cercarse. ¿Cuántos rollos de 200 m se requieren y su costo total?

See Solution

Problem 12

Il perimetro di un rettangolo è $51,8 \mathrm{~cm}$ e la lunghezza è $16,4 \mathrm{~cm}$ . Qual è la larghezza? R: 9,5 cm

See Solution

Problem 13

Calcola il perimetro di un rombo con lato $10,5 \mathrm{~cm}$ e il perimetro di un parallelogramo con lati $160 \mathrm{~cm}$ e $13,9 \mathrm{~dm}$ .

See Solution

Problem 14

Une piscine rectangulaire de 10 m sur 15 m est entourée d'une bande de gazon de $x$ m. Montre que la clôture fait $50 + 8x$ m et l'aire des allées de gazon est $50x + 4x^2$ . Calcule pour $x=2$ m.

See Solution

Problem 15

Find the area of a rectangle with one side $12 \mathrm{~cm}$ and diagonal $13 \mathrm{~cm}$ .

See Solution

Problem 16

Points A, B, C, and D divide segment AD in the ratio $2 \frac{1}{2}: 1 \frac{1}{3}: \frac{5}{6}$ ; AB = 30 cm. Find length of BD.

See Solution

Problem 17

Points A, B, C, and D divide segment AD in the ratio $2 \frac{1}{2}: 1 \frac{1}{3}: \frac{5}{6}$ . Given AB=30 cm, find BD. a. 26 cm b. 56 cm

See Solution

Problem 18

A model of an 800m tower is built at a scale of $1: 4000$ . What is the model's height? Options: 5cm, 20cm, 200cm, 320cm.

See Solution

Problem 19

A tower is 800 m tall. If a model is built at a scale of $1: 4000$ , what is the model's height?

See Solution

Problem 20

A model of an 800 m tower is built at a scale of $1:4000$ . What is the model's height? Options: 5 cm, 20 cm, 200 cm, 320 cm.

See Solution

Problem 21

A cylinder has a radius of $x$ cm and height $x + 3$ cm. Its surface area is $130 \pi$ cm². Find the quadratic in $x$ .

See Solution

Problem 22

Trova il lato di un quadrato isoperimetrico a un rettangolo di base $15 \mathrm{~cm}$ e altezza $24 \mathrm{~cm}$ . R: $19,5 \mathrm{~cm}$ . Inoltre, la somma e la differenza di due lati consecutivi di un rettangolo sono $75 \mathrm{~cm}$ e $17 \mathrm{~cm}$ .

See Solution

Problem 23

Find the area of a square (side 2) with a semi-circle on top. Options: a) $6+\pi$ , b) $2+\pi$ , c) $4+4\pi$ , d) $4+\frac{\pi}{2}$ , e) $4+\pi$ .

See Solution

Problem 24

Un quadrato è isoperimetrico a un rettangolo con base $15 \mathrm{~cm}$ e altezza $4 \mathrm{~cm}$ . Trova il lato del quadrato. R: $19,5 \mathrm{~cm}$

See Solution

Problem 25

36) Trova il lato di un quadrato isoperimetrico a un rettangolo di base $15 \mathrm{~cm}$ e altezza $24 \mathrm{~cm}$ . R: $19,5 \mathrm{~cm}$ 37) Due lati consecutivi di un rettangolo hanno somma $75 \mathrm{~cm}$ e differenza $17 \mathrm{~cm}$ .

See Solution

Problem 26

Calcola il perimetro di un esagono con lati congruenti: $15 \mathrm{~cm}$ , $21 \mathrm{~cm}$ e $7 \mathrm{~cm}$ . R: $78 \mathrm{~cm}$

See Solution

Problem 27

36) Trova il lato di un quadrato isoperimetrico a un rettangolo di base $15 \mathrm{~cm}$ e altezza $24 \mathrm{~cm}$ . R: $19,5 \mathrm{~cm}$ 37) Due lati consecutivi di un rettangolo hanno somma $75 \mathrm{~cm}$ e differenza $17 \mathrm{~cm}$ . Trova i lati. R: $46 \mathrm{~cm}, 29 \mathrm{~cm}$

See Solution

Problem 28

Правоъгьлен паралелепипед с размери $a, b, c$ има отношение $a:b=4:3$ и $b:c=2:5$ . Сборът на ръбовете е $232 \mathrm{~cm}$ . Какъв е обемът му?

See Solution

Problem 29

Calculate the area of a regular 7-sided polygon with an apothem of 8 m and side length of 7.7 m. Round to the nearest tenth. [?] $\mathrm{m}^{2}$

See Solution

Problem 30

Tasha's drawing shows piers $12 \mathrm{~cm}$ apart. If $2 \mathrm{~cm}$ = $0.5 \mathrm{mi}$ , find the actual distance between the piers.

See Solution

Problem 31

Find the perimeter of a rectangle with length 6 feet and width 3 feet. Use the formula $P = 2(l + w)$ .

See Solution

Problem 32

Emily's barn drawing is 15 in. wide and 18 in. long. If the actual width is 10 ft, find the actual length.

See Solution

Problem 33

Find the dimensions of a rectangle scaled by $\frac{2}{3}$ if the original is 12 inches long and 8 inches wide.

See Solution

Problem 34

Tentukan tinggi tiang silinder dengan isi padu $404 \mathrm{~cm}^{3}$ dan jejari $2 \mathrm{~cm}$ .

See Solution

Problem 35

Determine the length $L$ and width $W$ (where $W \leq L$ ) of a rectangle with perimeter 28 that maximizes area, then find that area.

See Solution

Problem 36

In parallelogram $A B C D$ , with $A B = B E = E C$ and area of triangle $B E C$ as 8, find the perimeter of polygon $A B E C D$ .

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Problem 37

A square frame has an outer perimeter of 28 and an inner perimeter of 20. Find the shortest distance between two vertices.

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Problem 38

Calculate the area of a regular 7-sided polygon with an apothem of 8 m and side length of 7.7 m. Round to the nearest tenth. $\text { [?] } \mathrm{m}^{2}$

See Solution

Problem 39

Compare the area of Priya's new figure (after cutting and attaching 4 squares) with the original square.

See Solution

Problem 40

Find the width of a rectangular playground with area 78 m² and length 13 m. Use the formula $A = l \times w$ .

See Solution

Problem 41

Una empresa fabrica peceras. Si el ancho es $x$ , ¿cuál es la expresión para el volumen en función de $x$ ?

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Problem 42

Calcula el volumen de una semiesfera con diámetro de 24 metros.

See Solution

Problem 43

Une piscine rectangulaire de 10m x 15m a une bande de gazon de $x$ m. Montre que la clôture mesure $50 + 8x$ .

See Solution

Problem 44

Find the actual area of a closet with dimensions $4.4 \mathrm{~cm}$ by $3.2 \mathrm{~cm}$ at a scale of $2 \mathrm{~cm}$ to $1 \mathrm{~m}$ .

See Solution

Problem 45

Find the dimensions of a scaled exercise mat if the actual area is $144 \mathrm{~m}^{2}$ and the scale is $8 \mathrm{~m}$ for every $2 \mathrm{in}$ .

See Solution

Problem 46

Francesca's mural is $12 \mathrm{ft}$ high and $135 \mathrm{ft}$ long. What are the dimensions of her scale drawing using $3 \mathrm{~cm}$ for every $4 \mathrm{ft}$ ?

See Solution

Problem 47

A $12.875-\mathrm{m}$ fence is one side of a rectangle. With $45.625 \mathrm{~m}$ left for the other sides, find the longer dimension.

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Problem 48

Find the area of parallelogram $ABCD$ with sides 6 and 4 units and an angle of 125 degrees. Compare it to 24.

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Problem 49

Francesca's mural is $12 \mathrm{ft}$ high and $135 \mathrm{ft}$ long. With a scale of $3 \mathrm{cm}$ for $4 \mathrm{ft}$ , find the drawing's dimensions.

See Solution

Problem 50

A scale drawing shows a closet measuring $4.4 \mathrm{~cm}$ by $3.2 \mathrm{~cm}$ . With a scale of $2 \mathrm{~cm}$ to $1 \mathrm{~m}$ , find the actual area.

See Solution

Problem 51

A rectangle has dimensions $10 \mathrm{~cm}$ by $8 \mathrm{~cm}$ . If length increases by $60\%$ , find width's percentage change if: (a) perimeter stays the same. (b) area stays the same.

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Problem 52

Calcula cuántos rollos de material necesita comprar para insonorizar 4 paredes de 2 m x 2.2 m, considerando una puerta de 0.8 m.

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Problem 53

Calcula el volumen de un archivador de $150 \mathrm{~cm}$ alto, $55 \mathrm{~cm}$ ancho y $60 \mathrm{~cm}$ fondo en m³.

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Problem 54

Find the radius of a sphere with volume $4.5 \mathrm{~m}^{3}$ using the formula $V=\frac{4}{3} \pi r^{3}$ .

See Solution

Problem 55

Find the length $L$ and width $W$ (with $W \leq L$ ) of a rectangle with perimeter 28 that maximizes area. What is the max area?

See Solution

Problem 56

Calculate the area of quadrilateral $ABCD$ with vertices $A(0,2)$ , $B(4,7)$ , $C(8,2)$ , $D(4,3)$ .

See Solution

Problem 57

Calculate the area of a parallelogram with base 6 inches and height 3 inches. Use the formula: Area = base × height = $6 \times 3$ .

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Problem 58

Find the area of a sector with radius 2 cm and central angle 90°, where OE = OF.

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Problem 59

Yair added sawdust to a toilet. The seat is $0.4 \mathrm{~m}$ above ground and the pit bottom is $1.5 \mathrm{~m}$ below.
1. Find the distance from the toilet seat to the pit bottom in $\mathrm{m}$ .
2. Calculate the height change of the sawdust from the seat to the pit bottom.

See Solution

Problem 60

Find the distance between Natasha's beagle at $\frac{25}{4}$ meters and her labrador at $\frac{51}{20}$ meters.

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Problem 61

A tank is 4.5 m long, 3.5 m wide, and 2.8 m deep. Water is pumped at 6500 L/h. After 3 hours, what is the water level from the top?

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Problem 62

What is the total cost of a rectangular plot measuring $1200 \mathrm{~m} \times 900 \mathrm{~m}$ if 1 hectare costs R5 200,00?

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Problem 63

Find the length of a side of square ABCD if its area is 89 cm². What is $\widehat{x}$ ?

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Problem 64

Calculate the volume of a hole measuring $11.0 \mathrm{~m} \times 14.5 \mathrm{~m} \times 4.0 \mathrm{~m}$ and a truck bed $4 \mathrm{~m} \times 3 \mathrm{~m} \times 2.0 \mathrm{~m}$ . How many trips needed?

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Problem 65

Find the area of the tiled walkway around a $24 \mathrm{ft} \times 12 \mathrm{ft}$ pool with a $2 \mathrm{ft}$ wide border.

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Problem 66

Find the map length of a road that is $3 \mathrm{~km}$ long, with a scale of $1: 120000$ . Answer in $\mathrm{cm}$ .

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Problem 67

Find the range of the actual area of a rectangle with width $3.0 \mathrm{~cm}$ and length $8.0 \mathrm{~cm}$ .

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Problem 68

Find the maximum absolute error for the measurements of an 8-sided polygon with given sides: $GF = 4cm$ , $FE = 3cm$ , $DC = 6cm$ , $CB = 8cm$ .

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Problem 69

In an 8-sided polygon $ABCDEFGH$ with rectangles $ABCD$ and $EFGH$ , find:
(a) max error in cm. (b) min area of rectangle $ABCD$ . (c) min area of rectangle $EFGH$ . (d) range of actual area $x$ in cm².

See Solution

Problem 70

Find the volume between a cone and a cube, with the cone's base inscribed in the cube's face. Use edge length $s$ .

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Problem 71

Find the perimeter of a rectangle with area $100 \mathrm{~m}^{2}$ as a function of one side's length.

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Problem 72

Find the length of the latus rectum and the parabolic arc for the parabola given by $x^{2}=4 a y$ .

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Problem 73

Find the length and width of a rectangular garden with area $96 \mathrm{~m}^{2}$ and perimeter $40 \mathrm{~m}$ .

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Problem 74

Find the equation of line $O A$ , show $A$ is $(16,-8)$ , and calculate area of trapezium $O A B C$ .

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Problem 75

Find the maximum load $P$ for an 8m beam with I section dimensions and stress limit of 340 MPa.

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Problem 76

Find the volume of a donut box with length 9 in, width 4 in, and height 3 in: $V = l \times w \times h$ .

See Solution

Problem 77

Find the volume of a donut box with dimensions: length = 9 in, width = 4 in, height = 3 in. Use $V = l \times w \times h$ .

See Solution

Problem 78

Find the volume of a rectangular prism with a base area of 20 unit cubes and 4 layers high.

See Solution

Problem 79

What is the volume of a rectangular prism with a base area of 20 unit cubes and a height of 4 layers?

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Problem 80

Penelope's Pizzeria has a pizza box volume of 12 cubic units. Which dimensions are possible? A. $1 \times 12 \times 1$ B. $3 \times 2 \times 2$ C. $6 \times 3 \times 1$

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Problem 81

What is the volume of a rectangular prism with a base area of 20 unit cubes and a height of 4 layers?

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Problem 82

Astiton compares two peanut boxes: Box 1 (base 14 in², height 7 in) and Box 2 (105 in³). Which has more volume?

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Problem 83

Astiton wants to buy the box of peanuts with the most volume. Compare Box 1 ( $14 \times 7$ ) and Box 2 ( $105$ ). Which is larger?

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Problem 84

Ashton needs to choose between two peanut boxes. Box \#1 has a volume of $14 \times 7 = 98$ cubic inches. Box \#2 is 105 cubic inches. Which box is larger?

See Solution

Problem 85

Locate points of rectangle $ABCD$ at $A(2,2), B(2,-1), C(-1,-1), D(-1,2)$ , then find its perimeter and area.

See Solution

Problem 86

Find the perimeter of a pentagon with sides 14, 12, 10, 8, and 6 inches using the expression $P = 14 + 12 + 10 + 8 + 6$ .

See Solution

Problem 87

César siembra un terreno cuadrado de 6 m en 20 min. ¿Cuánto tardará en sembrar uno de 12 m de lado?

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Problem 88

Punctele coliniare $A, B$ și $C$ au $B C=2 A C$ . Dacă $M$ și $N$ sunt mijloacele segmentelor $A C$ și $C B$ cu $M N=9 \mathrm{~cm}$ , găsește lungimea lui $A C$ : a) $3 \mathrm{~cm}$ ; b) $6 \mathrm{~cm}$ ; c) $18 \mathrm{~cm}$ .

See Solution

Problem 89

Hitung luas bilik dalam $\mathrm{cm}^{2}$ jika 250 jubin berukuran $6.096 \times 10^{2} \mathrm{~mm}$ dan $3.048 \times 10^{2} \mathrm{~mm}$ .

See Solution

Problem 90

Find a formula for the perimeter of a rectangle with area $100 \mathrm{~m}^{2}$ as a function of one side's length.

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Problem 91

Find the volume of a right cone with a base diameter of $9.5 \mathrm{~cm}$ and a height of $16 \mathrm{~cm}$ .

See Solution

Problem 92

In a pipeline with a 30 cm diameter and water speed of 1.5 m/s, find the speed at a 1 cm diameter.

See Solution

Problem 93

The office floor plan is at a scale of $1:20$ . Find the actual length for $96 \mathrm{~cm}$ and pantry area in $\mathrm{cm}^{2}$ for $4.8 \mathrm{~m}^{2}$ .

See Solution

Problem 94

In square $ABCD$ , area equals the sum of areas of triangles $ABE$ and $DCE$ . If $AB=6$ , find $CE$ . (a) 5 (b) 6 (c) 2 (d) 3 (e) 4

See Solution

Problem 95

In square $ABCD$ with $AB=6$ , the area equals the sum of triangles $ABE$ and $DCE$ . Find length of $CE$ .

See Solution

Problem 96

Find the area $x$ of hexagon $ABCDEF$ with rectangle $ABCD$ where $AB=9$ cm, $BC=16$ cm, $AE=8$ cm, and $FG=3$ cm.

See Solution

Problem 97

Berechne Volumen und Oberfläche einer Pyramide mit Grundfläche $a=15 \mathrm{~cm}, b=12 \mathrm{~cm}, h=20 \mathrm{~cm}$ .

See Solution

Problem 98

Clarence's garden is 20 ft by 40 ft. How many 4-yard fencing packages do they need for the perimeter?

See Solution

Problem 99

Berechne das Volumen und die Oberfläche eines Quaders mit $a=4 \mathrm{~cm}, b=6 \mathrm{~cm}, c=12 \mathrm{~cm}$ .

See Solution

Problem 100

Calculate the volume and surface area of a cube with side length 3 units. Use $V = s^3$ and $A = 6s^2$ .

See Solution

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Mensuration

Problem 1

Find the length of line segment AB AB AB where A A A and B B B are intersections of 2x+3y=6 2x + 3y = 6 2x+3y=6 and x2−2y2−xy=0 x^2 - 2y^2 - xy = 0 x2−2y2−xy=0.

Problem 2

Find the dimensions of a rectangle with area 21yd2 21 \mathrm{yd}^{2} 21yd2 and length 1yd 1 \mathrm{yd} 1yd less than twice the width.

Problem 3

Find the area between the curves y=3x2 y=3 x^{2} y=3x2, y=0 y=0 y=0, and x=3 x=3 x=3. Choose integration with respect to x x x or y y y.

Problem 4

已知半径为1的球体，求四棱锥体积最大时的高度选项：A. 13 \frac{1}{3} 31​ B. 12 \frac{1}{2} 21​ C. 33 \frac{\sqrt{3}}{3} 33​​ D. 22 \frac{\sqrt{2}}{2} 22​​

Problem 5

Find the apparent distance from the top of a 4.20 cm benzene layer to the bottom of a 6.20 cm water layer at normal incidence.

Problem 6

A mud house has a cone roof over a cylinder. Given dimensions, find AB A B AB, volume, surface area, and house choice.

Problem 7

Find the volume of a cuboid with face areas 35 cm235 \mathrm{~cm}^{2}35 cm2, 42 cm242 \mathrm{~cm}^{2}42 cm2, and 14 cm214 \mathrm{~cm}^{2}14 cm2.

Problem 8

Calculate the inductance and capacitance per phase of a 40 km overhead line with copper conductors (1.5 cm diameter) in two spacings: 75 cm flat and triangular sides 70 cm, 90 cm, 110 cm.

Problem 9

A rectangle has a length of 4 times its width and an area of 16. Find its perimeter. A. 8 B. 10 C. 20 D. 32

Problem 10

Съществува десетоъгълна призма с периметър на основата 30 cm30 \mathrm{~cm}30 cm и околен ръб 8 cm8 \mathrm{~cm}8 cm. Намерете сбора на ръбовете в см.

Problem 11

Una finca rectangular de 187 m de largo y 87 m de ancho necesita cercarse. ¿Cuántos rollos de 200 m se requieren y su costo total?

Problem 12

Il perimetro di un rettangolo è 51,8 cm51,8 \mathrm{~cm}51,8 cm e la lunghezza è 16,4 cm16,4 \mathrm{~cm}16,4 cm. Qual è la larghezza? R: 9,5 cm

Problem 13

Calcola il perimetro di un rombo con lato 10,5 cm10,5 \mathrm{~cm}10,5 cm e il perimetro di un parallelogramo con lati 160 cm160 \mathrm{~cm}160 cm e 13,9 dm13,9 \mathrm{~dm}13,9 dm.

Problem 14

Une piscine rectangulaire de 10 m sur 15 m est entourée d'une bande de gazon de xxx m. Montre que la clôture fait 50+8x50 + 8x50+8x m et l'aire des allées de gazon est 50x+4x250x + 4x^250x+4x2. Calcule pour x=2x=2x=2 m.

Problem 15

Find the area of a rectangle with one side 12 cm12 \mathrm{~cm}12 cm and diagonal 13 cm13 \mathrm{~cm}13 cm.

Problem 16

Points A, B, C, and D divide segment AD in the ratio 212:113:562 \frac{1}{2}: 1 \frac{1}{3}: \frac{5}{6}221​:131​:65​; AB = 30 cm. Find length of BD.

Problem 17

Points A, B, C, and D divide segment AD in the ratio 212:113:562 \frac{1}{2}: 1 \frac{1}{3}: \frac{5}{6}221​:131​:65​. Given AB=30 cm, find BD. a. 26 cm b. 56 cm

Problem 18

A model of an 800m tower is built at a scale of 1:40001: 40001:4000. What is the model's height? Options: 5cm, 20cm, 200cm, 320cm.

Problem 19

A tower is 800 m tall. If a model is built at a scale of 1:40001: 40001:4000, what is the model's height?

Problem 20

A model of an 800 m tower is built at a scale of 1:40001:40001:4000. What is the model's height? Options: 5 cm, 20 cm, 200 cm, 320 cm.

Problem 21

A cylinder has a radius of xxx cm and height x+3x + 3x+3 cm. Its surface area is 130π130 \pi130π cm². Find the quadratic in xxx.

Problem 22

Problem 23

Find the area of a square (side 2) with a semi-circle on top. Options: a) 6+π6+\pi6+π, b) 2+π2+\pi2+π, c) 4+4π4+4\pi4+4π, d) 4+π24+\frac{\pi}{2}4+2π​, e) 4+π4+\pi4+π.

Problem 24

Un quadrato è isoperimetrico a un rettangolo con base 15 cm15 \mathrm{~cm}15 cm e altezza 4 cm4 \mathrm{~cm}4 cm. Trova il lato del quadrato. R: 19,5 cm19,5 \mathrm{~cm}19,5 cm

Problem 25

36) Trova il lato di un quadrato isoperimetrico a un rettangolo di base 15 cm15 \mathrm{~cm}15 cm e altezza 24 cm24 \mathrm{~cm}24 cm. R: 19,5 cm19,5 \mathrm{~cm}19,5 cm 37) Due lati consecutivi di un rettangolo hanno somma 75 cm75 \mathrm{~cm}75 cm e differenza 17 cm17 \mathrm{~cm}17 cm.

Problem 26

Calcola il perimetro di un esagono con lati congruenti: 15 cm15 \mathrm{~cm}15 cm, 21 cm21 \mathrm{~cm}21 cm e 7 cm7 \mathrm{~cm}7 cm. R: 78 cm78 \mathrm{~cm}78 cm

Problem 27

Problem 28

Правоъгьлен паралелепипед с размери a,b,ca, b, ca,b,c има отношение a:b=4:3a:b=4:3a:b=4:3 и b:c=2:5b:c=2:5b:c=2:5. Сборът на ръбовете е 232 cm232 \mathrm{~cm}232 cm. Какъв е обемът му?

Problem 29

Calculate the area of a regular 7-sided polygon with an apothem of 8 m and side length of 7.7 m. Round to the nearest tenth. [?] m2\mathrm{m}^{2}m2

Problem 30

Tasha's drawing shows piers 12 cm12 \mathrm{~cm}12 cm apart. If 2 cm2 \mathrm{~cm}2 cm = 0.5mi0.5 \mathrm{mi}0.5mi, find the actual distance between the piers.

Problem 31

Find the perimeter of a rectangle with length 6 feet and width 3 feet. Use the formula P=2(l+w)P = 2(l + w)P=2(l+w).

Problem 32

Emily's barn drawing is 15 in. wide and 18 in. long. If the actual width is 10 ft, find the actual length.

Problem 33

Find the dimensions of a rectangle scaled by 23\frac{2}{3}32​ if the original is 12 inches long and 8 inches wide.

Problem 34

Tentukan tinggi tiang silinder dengan isi padu 404 cm3404 \mathrm{~cm}^{3}404 cm3 dan jejari 2 cm2 \mathrm{~cm}2 cm.

Problem 35

Determine the length LLL and width WWW (where W≤LW \leq LW≤L) of a rectangle with perimeter 28 that maximizes area, then find that area.

Problem 36

In parallelogram ABCDA B C DABCD, with AB=BE=ECA B = B E = E CAB=BE=EC and area of triangle BECB E CBEC as 8, find the perimeter of polygon ABECDA B E C DABECD.

Problem 37

A square frame has an outer perimeter of 28 and an inner perimeter of 20. Find the shortest distance between two vertices.

Problem 38

Calculate the area of a regular 7-sided polygon with an apothem of 8 m and side length of 7.7 m. Round to the nearest tenth. [?] m2\text { [?] } \mathrm{m}^{2} [?] m2

Problem 39

Compare the area of Priya's new figure (after cutting and attaching 4 squares) with the original square.

Problem 40

Find the width of a rectangular playground with area 78 m² and length 13 m. Use the formula A=l×wA = l \times wA=l×w.

Problem 41

Find the length of line segment $AB$ where $A$ and $B$ are intersections of $2x + 3y = 6$ and $x^2 - 2y^2 - xy = 0$ .

Find the dimensions of a rectangle with area $21 \mathrm{yd}^{2}$ and length $1 \mathrm{yd}$ less than twice the width.

Find the area between the curves $y=3 x^{2}$ , $y=0$ , and $x=3$ . Choose integration with respect to $x$ or $y$ .

已知半径为1的球体，求四棱锥体积最大时的高度选项：A. $\frac{1}{3}$ B. $\frac{1}{2}$ C. $\frac{\sqrt{3}}{3}$ D. $\frac{\sqrt{2}}{2}$

A mud house has a cone roof over a cylinder. Given dimensions, find $A B$ , volume, surface area, and house choice.

Find the volume of a cuboid with face areas $35 \mathrm{~cm}^{2}$ , $42 \mathrm{~cm}^{2}$ , and $14 \mathrm{~cm}^{2}$ .

Съществува десетоъгълна призма с периметър на основата $30 \mathrm{~cm}$ и околен ръб $8 \mathrm{~cm}$ . Намерете сбора на ръбовете в см.

Il perimetro di un rettangolo è $51,8 \mathrm{~cm}$ e la lunghezza è $16,4 \mathrm{~cm}$ . Qual è la larghezza? R: 9,5 cm

Calcola il perimetro di un rombo con lato $10,5 \mathrm{~cm}$ e il perimetro di un parallelogramo con lati $160 \mathrm{~cm}$ e $13,9 \mathrm{~dm}$ .

Une piscine rectangulaire de 10 m sur 15 m est entourée d'une bande de gazon de $x$ m. Montre que la clôture fait $50 + 8x$ m et l'aire des allées de gazon est $50x + 4x^2$ . Calcule pour $x=2$ m.

Find the area of a rectangle with one side $12 \mathrm{~cm}$ and diagonal $13 \mathrm{~cm}$ .

Points A, B, C, and D divide segment AD in the ratio $2 \frac{1}{2}: 1 \frac{1}{3}: \frac{5}{6}$ ; AB = 30 cm. Find length of BD.

Points A, B, C, and D divide segment AD in the ratio $2 \frac{1}{2}: 1 \frac{1}{3}: \frac{5}{6}$ . Given AB=30 cm, find BD. a. 26 cm b. 56 cm

A model of an 800m tower is built at a scale of $1: 4000$ . What is the model's height? Options: 5cm, 20cm, 200cm, 320cm.

A tower is 800 m tall. If a model is built at a scale of $1: 4000$ , what is the model's height?

A model of an 800 m tower is built at a scale of $1:4000$ . What is the model's height? Options: 5 cm, 20 cm, 200 cm, 320 cm.

A cylinder has a radius of $x$ cm and height $x + 3$ cm. Its surface area is $130 \pi$ cm². Find the quadratic in $x$ .

Find the area of a square (side 2) with a semi-circle on top. Options: a) $6+\pi$ , b) $2+\pi$ , c) $4+4\pi$ , d) $4+\frac{\pi}{2}$ , e) $4+\pi$ .

Un quadrato è isoperimetrico a un rettangolo con base $15 \mathrm{~cm}$ e altezza $4 \mathrm{~cm}$ . Trova il lato del quadrato. R: $19,5 \mathrm{~cm}$

36) Trova il lato di un quadrato isoperimetrico a un rettangolo di base $15 \mathrm{~cm}$ e altezza $24 \mathrm{~cm}$ . R: $19,5 \mathrm{~cm}$ 37) Due lati consecutivi di un rettangolo hanno somma $75 \mathrm{~cm}$ e differenza $17 \mathrm{~cm}$ .

Calcola il perimetro di un esagono con lati congruenti: $15 \mathrm{~cm}$ , $21 \mathrm{~cm}$ e $7 \mathrm{~cm}$ . R: $78 \mathrm{~cm}$

Правоъгьлен паралелепипед с размери $a, b, c$ има отношение $a:b=4:3$ и $b:c=2:5$ . Сборът на ръбовете е $232 \mathrm{~cm}$ . Какъв е обемът му?

Calculate the area of a regular 7-sided polygon with an apothem of 8 m and side length of 7.7 m. Round to the nearest tenth. [?] $\mathrm{m}^{2}$

Tasha's drawing shows piers $12 \mathrm{~cm}$ apart. If $2 \mathrm{~cm}$ = $0.5 \mathrm{mi}$ , find the actual distance between the piers.

Find the perimeter of a rectangle with length 6 feet and width 3 feet. Use the formula $P = 2(l + w)$ .

Find the dimensions of a rectangle scaled by $\frac{2}{3}$ if the original is 12 inches long and 8 inches wide.

Tentukan tinggi tiang silinder dengan isi padu $404 \mathrm{~cm}^{3}$ dan jejari $2 \mathrm{~cm}$ .

Determine the length $L$ and width $W$ (where $W \leq L$ ) of a rectangle with perimeter 28 that maximizes area, then find that area.

In parallelogram $A B C D$ , with $A B = B E = E C$ and area of triangle $B E C$ as 8, find the perimeter of polygon $A B E C D$ .

Calculate the area of a regular 7-sided polygon with an apothem of 8 m and side length of 7.7 m. Round to the nearest tenth. $\text { [?] } \mathrm{m}^{2}$

Find the width of a rectangular playground with area 78 m² and length 13 m. Use the formula $A = l \times w$ .

Una empresa fabrica peceras. Si el ancho es $x$ , ¿cuál es la expresión para el volumen en función de $x$ ?

Une piscine rectangulaire de 10m x 15m a une bande de gazon de $x$ m. Montre que la clôture mesure $50 + 8x$ .

Find the actual area of a closet with dimensions $4.4 \mathrm{~cm}$ by $3.2 \mathrm{~cm}$ at a scale of $2 \mathrm{~cm}$ to $1 \mathrm{~m}$ .

Find the dimensions of a scaled exercise mat if the actual area is $144 \mathrm{~m}^{2}$ and the scale is $8 \mathrm{~m}$ for every $2 \mathrm{in}$ .

Francesca's mural is $12 \mathrm{ft}$ high and $135 \mathrm{ft}$ long. What are the dimensions of her scale drawing using $3 \mathrm{~cm}$ for every $4 \mathrm{ft}$ ?

A $12.875-\mathrm{m}$ fence is one side of a rectangle. With $45.625 \mathrm{~m}$ left for the other sides, find the longer dimension.

Find the area of parallelogram $ABCD$ with sides 6 and 4 units and an angle of 125 degrees. Compare it to 24.

Francesca's mural is $12 \mathrm{ft}$ high and $135 \mathrm{ft}$ long. With a scale of $3 \mathrm{cm}$ for $4 \mathrm{ft}$ , find the drawing's dimensions.

A scale drawing shows a closet measuring $4.4 \mathrm{~cm}$ by $3.2 \mathrm{~cm}$ . With a scale of $2 \mathrm{~cm}$ to $1 \mathrm{~m}$ , find the actual area.

A rectangle has dimensions $10 \mathrm{~cm}$ by $8 \mathrm{~cm}$ . If length increases by $60\%$ , find width's percentage change if: (a) perimeter stays the same. (b) area stays the same.

Calcula el volumen de un archivador de $150 \mathrm{~cm}$ alto, $55 \mathrm{~cm}$ ancho y $60 \mathrm{~cm}$ fondo en m³.

Find the radius of a sphere with volume $4.5 \mathrm{~m}^{3}$ using the formula $V=\frac{4}{3} \pi r^{3}$ .

Find the length $L$ and width $W$ (with $W \leq L$ ) of a rectangle with perimeter 28 that maximizes area. What is the max area?

Calculate the area of quadrilateral $ABCD$ with vertices $A(0,2)$ , $B(4,7)$ , $C(8,2)$ , $D(4,3)$ .

Calculate the area of a parallelogram with base 6 inches and height 3 inches. Use the formula: Area = base × height = $6 \times 3$ .

Yair added sawdust to a toilet. The seat is $0.4 \mathrm{~m}$ above ground and the pit bottom is $1.5 \mathrm{~m}$ below.
1. Find the distance from the toilet seat to the pit bottom in $\mathrm{m}$ .
2. Calculate the height change of the sawdust from the seat to the pit bottom.

Find the distance between Natasha's beagle at $\frac{25}{4}$ meters and her labrador at $\frac{51}{20}$ meters.

What is the total cost of a rectangular plot measuring $1200 \mathrm{~m} \times 900 \mathrm{~m}$ if 1 hectare costs R5 200,00?

Find the length of a side of square ABCD if its area is 89 cm². What is $\widehat{x}$ ?

Calculate the volume of a hole measuring $11.0 \mathrm{~m} \times 14.5 \mathrm{~m} \times 4.0 \mathrm{~m}$ and a truck bed $4 \mathrm{~m} \times 3 \mathrm{~m} \times 2.0 \mathrm{~m}$ . How many trips needed?

Find the area of the tiled walkway around a $24 \mathrm{ft} \times 12 \mathrm{ft}$ pool with a $2 \mathrm{ft}$ wide border.

Find the map length of a road that is $3 \mathrm{~km}$ long, with a scale of $1: 120000$ . Answer in $\mathrm{cm}$ .

Find the range of the actual area of a rectangle with width $3.0 \mathrm{~cm}$ and length $8.0 \mathrm{~cm}$ .

Find the maximum absolute error for the measurements of an 8-sided polygon with given sides: $GF = 4cm$ , $FE = 3cm$ , $DC = 6cm$ , $CB = 8cm$ .

In an 8-sided polygon $ABCDEFGH$ with rectangles $ABCD$ and $EFGH$ , find:
(a) max error in cm. (b) min area of rectangle $ABCD$ . (c) min area of rectangle $EFGH$ . (d) range of actual area $x$ in cm².

Find the volume between a cone and a cube, with the cone's base inscribed in the cube's face. Use edge length $s$ .

Find the perimeter of a rectangle with area $100 \mathrm{~m}^{2}$ as a function of one side's length.

Find the length of the latus rectum and the parabolic arc for the parabola given by $x^{2}=4 a y$ .

Find the length and width of a rectangular garden with area $96 \mathrm{~m}^{2}$ and perimeter $40 \mathrm{~m}$ .

Find the equation of line $O A$ , show $A$ is $(16,-8)$ , and calculate area of trapezium $O A B C$ .