9.4 Use Properties of Rectangles, Triangles, and Trapezoids

Telling linear from square from cubic measure, then perimeter and area formulas for rectangles, triangles, and trapezoids applied to fencing and flooring.

Prealgebra 2e, 9.4 Use Properties of Rectangles, Triangles, and Trapezoids

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74 exercises

9.4 Exercise 1

Before you get started, take this readiness quiz.

The length of a rectangle is $3$ less than the width. Let $w$ represent the width. Write an expression for the length of the rectangle.
If you missed this problem, review the reference.

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9.4 Exercise 2

Simplify: $\frac{1}{2} \left(6 h\right) .$
If you missed this problem, review the reference.

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9.4 Exercise 3

Simplify: $\frac{5}{2} \left(10.3 - 7.9\right) .$
If you missed this problem, review the reference.

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9.4 Exercise 4

For each item, state whether you would use linear, square, or cubic measure:

ⓐ amount of carpeting needed in a room
ⓑ extension cord length
ⓒ amount of sand in a sandbox
ⓓ length of a curtain rod
ⓔ amount of flour in a canister
ⓕ size of the roof of a doghouse.

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9.4 Exercise 5

Determine whether you would use linear, square, or cubic measure for each item.

ⓐ amount of paint in a can ⓑ height of a tree ⓒ floor of your bedroom ⓓ diameter of bike wheel ⓔ size of a piece of sod ⓕ amount of water in a swimming pool

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9.4 Exercise 6

Determine whether you would use linear, square, or cubic measure for each item.

ⓐ volume of a packing box ⓑ size of patio ⓒ amount of medicine in a syringe ⓓ length of a piece of yarn ⓔ size of housing lot ⓕ height of a flagpole

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9.4 Exercise 11

The length of a rectangle is $120$ yards and the width is $50$ yards. Find ⓐ the perimeter and ⓑ the area.

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9.4 Exercise 12

The length of a rectangle is $62$ feet and the width is $48$ feet. Find ⓐ the perimeter and ⓑ the area.

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9.4 Exercise 14

Find the length of a rectangle with a perimeter of $80$ inches and width of $25$ inches.

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9.4 Exercise 15

Find the length of a rectangle with a perimeter of $30$ yards and width of $6$ yards.

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9.4 Exercise 17

The width of a rectangle is seven meters less than the length. The perimeter is $58$ meters. Find the length and width.

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9.4 Exercise 18

The length of a rectangle is eight feet more than the width. The perimeter is $60$ feet. Find the length and width.

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9.4 Exercise 20

The length of a rectangle is eight more than twice the width. The perimeter is $64$ feet. Find the length and width.

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9.4 Exercise 21

The width of a rectangle is six less than twice the length. The perimeter is $18$ centimeters. Find the length and width.

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9.4 Exercise 23

The area of a rectangle is $598$ square feet. The length is $23$ feet. What is the width?

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9.4 Exercise 24

The width of a rectangle is $21$ meters. The area is $609$ square meters. What is the length?

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9.4 Exercise 26

The perimeter of a rectangular swimming pool is $200$ feet. The length is $40$ feet more than the width. Find the length and width.

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9.4 Exercise 27

The length of a rectangular garden is $30$ yards more than the width. The perimeter is $300$ yards. Find the length and width.

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9.4 Exercise 29

Find the area of a triangle with base $13$ inches and height $2$ inches.

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9.4 Exercise 30

Find the area of a triangle with base $14$ inches and height $7$ inches.

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9.4 Exercise 32

The perimeter of a triangular garden is $48$ feet. The lengths of two sides are $18$ feet and $22$ feet. How long is the third side?

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9.4 Exercise 33

The lengths of two sides of a triangular window are $7$ feet and $5$ feet. The perimeter is $18$ feet. How long is the third side?

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9.4 Exercise 35

The area of a triangular painting is $126$ square inches. The base is $18$ inches. What is the height?

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9.4 Exercise 36

A triangular tent door has an area of $15$ square feet. The height is $5$ feet. What is the base?

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9.4 Exercise 38

Find the length of each side of an equilateral triangle with perimeter $39$ inches.

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9.4 Exercise 39

Find the length of each side of an equilateral triangle with perimeter $51$ centimeters.

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9.4 Exercise 41

A backyard deck is in the shape of an isosceles triangle with a base of $20$ feet. The perimeter of the deck is $48$ feet. How long is each of the equal sides of the deck?

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9.4 Exercise 42

A boat’s sail is an isosceles triangle with base of $8$ meters. The perimeter is $22$ meters. How long is each of the equal sides of the sail?

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9.4 Exercise 44

The height of a trapezoid is $14$ yards and the bases are $7$ and $16$ yards. What is the area?

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9.4 Exercise 45

The height of a trapezoid is $18$ centimeters and the bases are $17$ and $8$ centimeters. What is the area?

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9.4 Exercise 47

The height of a trapezoid is $7$ centimeters and the bases are $4.6$ and $7.4$ centimeters. What is the area?

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9.4 Exercise 48

The height of a trapezoid is $9$ meters and the bases are $6.2$ and $7.8$ meters. What is the area?

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9.4 Exercise 50

Lin wants to sod his lawn, which is shaped like a trapezoid. The bases are $10.8$ yards and $6.7$ yards, and the height is $4.6$ yards. How many square yards of sod does he need?

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9.4 Exercise 51

Kira wants cover his patio with concrete pavers. If the patio is shaped like a trapezoid whose bases are $18$ feet and $14$ feet and whose height is $15$ feet, how many square feet of pavers will he need?

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9.4 Exercise 52

Determine whether you would measure each item using linear, square, or cubic units.

amount of water in a fish tank

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9.4 Exercise 54

Determine whether you would measure each item using linear, square, or cubic units.

living area of an apartment

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9.4 Exercise 56

Determine whether you would measure each item using linear, square, or cubic units.

height of a doorway

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9.4 Exercise 64

Find the ⓐ perimeter and ⓑ area of each rectangle.

The length of a rectangle is $85$ feet and the width is $45$ feet.

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9.4 Exercise 66

Find the ⓐ perimeter and ⓑ area of each rectangle.

A rectangular room is $15$ feet wide by $14$ feet long.

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9.4 Exercise 68

Solve.

Find the length of a rectangle with perimeter $124$ inches and width $38$ inches.

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9.4 Exercise 70

Solve.

Find the width of a rectangle with perimeter $92$ meters and length $19$ meters.

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9.4 Exercise 72

Solve.

The area of a rectangle is $414$ square meters. The length is $18$ meters. What is the width?

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9.4 Exercise 74

Solve.

The length of a rectangle is $9$ inches more than the width. The perimeter is $46$ inches. Find the length and the width.

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9.4 Exercise 76

Solve.

The perimeter of a rectangle is $58$ meters. The width of the rectangle is $5$ meters less than the length. Find the length and the width of the rectangle.

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9.4 Exercise 78

Solve.

The width of the rectangle is $0.7$ meters less than the length. The perimeter of a rectangle is $52.6$ meters. Find the dimensions of the rectangle.

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9.4 Exercise 80

Solve.

The perimeter of a rectangle of $150$ feet. The length of the rectangle is twice the width. Find the length and width of the rectangle.

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9.4 Exercise 82

Solve.

The length of a rectangle is $3$ meters less than twice the width. The perimeter is $36$ meters. Find the length and width.

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9.4 Exercise 84

Solve.

The width of a rectangular window is $24$ inches. The area is $624$ square inches. What is the length?

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9.4 Exercise 86

Solve.

The area of a rectangular roof is $2310$ square meters. The length is $42$ meters. What is the width?

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9.4 Exercise 88

Solve.

The perimeter of a rectangular courtyard is $160$ feet. The length is $10$ feet more than the width. Find the length and the width.

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9.4 Exercise 90

Solve.

The width of a rectangular window is $40$ inches less than the height. The perimeter of the doorway is $224$ inches. Find the length and the width.

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