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Geometry

Ray C. Jurgensen,Richard G. Brown,John W. Jurgensen

Chapter 11

Areas of Plane Figures

Educators

EM

Problem 1

Exercises $1-16$ refer to rectangles. Complete the tables. $p$ is the perimeter.

Amrita B.
Numerade Educator

Problem 2

Exercises $1-16$ refer to rectangles. Complete the tables. $p$ is the perimeter.

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Problem 3

Exercises $1-16$ refer to rectangles. Complete the tables. $p$ is the perimeter.

Amrita B.
Numerade Educator

Problem 4

Exercises $1-16$ refer to rectangles. Complete the tables. $p$ is the perimeter.

Check back soon!

Problem 5

Exercises $1-16$ refer to rectangles. Complete the tables. $p$ is the perimeter.

Amrita B.
Numerade Educator

Problem 6

Exercises $1-16$ refer to rectangles. Complete the tables. $p$ is the perimeter.

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Problem 7

Exercises $1-16$ refer to rectangles. Complete the tables. $p$ is the perimeter.

Amrita B.
Numerade Educator

Problem 8

Exercises $1-16$ refer to rectangles. Complete the tables. $p$ is the perimeter.

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Problem 9

Exercises $1-16$ refer to rectangles. Complete the tables. $p$ is the perimeter.

Amrita B.
Numerade Educator

Problem 10

Exercises $1-16$ refer to rectangles. Complete the tables. $p$ is the perimeter.

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Problem 11

Exercises $1-16$ refer to rectangles. Complete the tables. $p$ is the perimeter.

Amrita B.
Numerade Educator

Problem 12

Exercises $1-16$ refer to rectangles. Complete the tables. $p$ is the perimeter.

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Problem 13

Exercises $1-16$ refer to rectangles. Complete the tables. $p$ is the perimeter.

Amrita B.
Numerade Educator

Problem 14

Exercises $1-16$ refer to rectangles. Complete the tables. $p$ is the perimeter.

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Problem 15

Exercises $1-16$ refer to rectangles. Complete the tables. $p$ is the perimeter.

Amrita B.
Numerade Educator

Problem 16

Exercises $1-16$ refer to rectangles. Complete the tables. $p$ is the perimeter.

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Problem 17

Consecutive sides of the figures are perpendicular. Find the area of each figure.

Amrita B.
Numerade Educator

Problem 18

Consecutive sides of the figures are perpendicular. Find the area of each figure.

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Problem 19

Consecutive sides of the figures are perpendicular. Find the area of each figure.

Amrita B.
Numerade Educator

Problem 20

Consecutive sides of the figures are perpendicular. Find the area of each figure.

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Problem 21

Consecutive sides of the figures are perpendicular. Find the area of each figure.

Amrita B.
Numerade Educator

Problem 22

Consecutive sides of the figures are perpendicular. Find the area of each figure.

EM
Elisa M.
Numerade Educator

Problem 23

In Exercises 23 and 24 find each area in terms of the variables.

Amrita B.
Numerade Educator

Problem 24

In Exercises 23 and 24 find each area in terms of the variables.

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Problem 25

Find the area of a square with diagonals of length $d$ .

Amrita B.
Numerade Educator

Problem 26

The length of a rectangle is 12 $\mathrm{cm}$ more than its width. Find the area of the rectangle if its perimeter is 100 $\mathrm{cm}$ .

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Problem 27

A path 2 $\mathrm{m}$ wide surrounds a rectangular garden 20 $\mathrm{m}$ long and 12 $\mathrm{m}$ wide. Find the area of the path.

Amrita B.
Numerade Educator

Problem 28

How much will it cost to blacktop the driveway shown if blacktopping costs $\$ 11.00$ per square meter?

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Problem 29

A room 28 ft long and 20 ft wide has walls 8 ft high.
a. What is the total wall area?
b. How many gallon cans of paint should be bought to paint the walls if 1 gal of paint covers 300 $\mathrm{ft}^{2}$ ?

Amrita B.
Numerade Educator

Problem 30

A wooden fence 6 ft high and 220 ft long is to be painted on both sides.
a. What is the total area to be painted?
b. A gallon of a certain type of paint will cover only 200 $\mathrm{ft}^{2}$ of area for the first coat, but on the second coat a gallon of the same paint will cover 300 $\mathrm{ft}^{2}$ . If the fence is to be given two coats of paint, how many gallons of paint should be bought?

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Problem 31

A rectangle having area 392 $\mathrm{m}^{2}$ is twice as long as it is wide. Find its dimensions.

Amrita B.
Numerade Educator

Problem 32

The lengths of the sides of three squares are $s, s+1,$ and $s+2$ If their total area is $365 \mathrm{cm}^{2},$ find their total perimeter.

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Problem 33

Derive a formula for the area of the triangle shown by using the formula for the area of a rectangle.

Amrita B.
Numerade Educator

Problem 34

The diagonals of a rectangle are 18 $\mathrm{cm}$ long and intersect at a $60^{\circ}$ angle. Find the area of the rectangle.

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Problem 35

a. Suppose you have 40 $\mathrm{m}$ of fencing with which to make a rectangular pen for a dog. If one side of the rectangle is $x \mathrm{m}$ long, explain why the other side is $(20-x) \mathrm{m}$ long.
b. Express the area of the pen in terms of $x$ .
c. Find the area of the pen for each value of $x : 0,2$ $4,6,8,10,12,14,16,18,20 .$ Record your answers
on a set of axes like the one shown.
d. Give the dimensions of the pen with the greatest area.

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Problem 36

A farmer has 100 $\mathrm{m}$ of fencing with which to make a rectangular corral. A side of a barn will be used as one side of the corral, as shown in the overhead view.
a. If the width of the corral is $x$ , express the length and the area in terms of $x$ .
b. Make a graph showing values of $x$ on the horizontal axis and the corresponding areas on the vertical axis.
c. What dimensions give the corral the greatest possible area?

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Problem 37

Draw a rectangle. Then construct a square with equal area.

Amrita B.
Numerade Educator