424 Chapter 8 Polygons and Area
Goal
Find the area of squares
and rectangles.
Key Words
• area
• square p. 325
• rectangle p. 325
Can you tell which of the rectangles below covers more surface?
Rectangle A is made up of 18 squares while rectangle B is made
up of 20 squares. So, rectangle B covers more area. The amount
of surface covered by a figure is its .
Area is measured in square units such as square inches (in.
2
)
and square meters (m
2
).
area
8.3
8.3
Area of Squares and
Rectangles
Find the area of the square.
Solution
Use the formula for the area of
a square and substitute 9 for s.
A 5
s
2
Formula for the area of a square
5 9
2
Substitute 9 for s.
5 81 Simplify.
ANSWER
©
The area of the square is 81 square feet.
EXAMPLE
1
Find the Area of a Square
A B
9 ft
Words Area 5 (side)
2
Symbols A 5 s
2
AREA OF A SQUARE
s
Page 1 of 6
8.3 Area of Squares and Rectangles 425
Words Area 5 (base)(height)
Symbols A 5 bh
AREA OF A RECTANGLE
Find the area of the rectangular pool.
Solution
Use the formula for the area of a
rectangle. Substitute 24 for b and
16 for h.
A 5 bh
Formula for the area of a rectangle
5 24 p 16 Substitute 24 for b and 16 for h.
5 384 Multiply.
ANSWER
©
The area of the pool is 384 square feet.
EXAMPLE
2
Find the Area of a Rectangle
The rectangle has an area of 54 square inches.
Find its height.
Solution
Use the formula for the area of a rectangle
and substitute 54 for A and 9 for b.
A 5 bh Formula for the area of a rectangle
54 5 9h Substitute 54 for A and 9 for b.
6 5 h Divide each side by 9.
ANSWER
©
The height of the rectangle is 6 inches.
EXAMPLE
3
Find the Height of a Rectangle
height, h
base, b
24 ft
16 ft
h
9 in.
A 5 54 in.
2
Find the area of the quadrilateral.
1. 2. 3.
4.
A rectangle has an area of 52 square meters and a height of
4 meters. Find the length of its base.
4.5 yd
5.9 yd
2 ft
6 ft
11 m
Area of Squares and Rectangles
M
ORE
E
XAMPLES
More examples at
classzone
.com
IStudent Help
I C L A S S Z O N E . C O M
Page 2 of 6
426 Chapter 8 Polygons and Area
To find the area of a complex polygon, divide the polygon into smaller
regions whose areas you can find.
Find the area of the polygon made up of rectangles.
5. 6.
12 m
4 m
6 m
3 m
5 m
3 m
Polygons Made Up of Rectangles
Find the dimensions of rectangles A and B.
Solution
Rectangle A
The base is 5 units.
Because rectangle B is 2 units taller than
rectangle A, the height of rectangle A is
7 2 2 5 5 units.
Rectangle B
The height is 7 units.
The base of rectangle B is the total of
both bases minus the base of rectangle A,
or 9 2 5 5 4 units.
EXAMPLE
4
Divide a Complex Polygon into Rectangles
Find the area of the polygon made up of rectangles.
Solution
Add the areas of the rectangles.
Area 5 Area of F 1 Area of G 1 Area of H
5 bh 1 bh 1 bh
5 4 p 3 1 (7 2 4) p (9 2 2) 1 5 p 2
5 4 p 3 1 3 p 7 1 5 p 2
5 12 1 21 1 10
5 43
ANSWER
©
The total area of the polygon is 43 square centimeters.
EXAMPLE
5
Find the Area of a Complex Polygon
9
7
2
5
A
B
9
7
4
2
5
A
B
5
9 cm
7 cm
5 cm
4 cm
2 cm
3 cm
2 cm
F
G
H
Labels on diagrams
are centered on the
segment with which
they correspond.
In Example 5, the 9 cm
label refers to a side of
the polygon, not just the
height of rectangle G.
Visualize It!
Page 3 of 6
8.3 Area of Squares and Rectangles 427
Exercises
8.3
8.3
Extra Practice
See p. 689.
1. What kind of quadrilateral has opposite sides parallel, opposite
sides congruent, and four right angles?
Match the figure with the corresponding area equation.
A. A 5 x
2
B. A 5 2x
2
C. A 5 4x
2
2. 3. 4.
Determine whether the statement about the diagram is true or false.
Explain your answer.
5. To find the area of the entire polygon, add
the areas of the three rectangles.
6. The height of rectangle A is 1 unit.
7. The height of rectangle C is 5 units.
Area of a Square
Find the area of the square.
8. 9. 10.
Area of a Rectangle
Find the area of the rectangle.
11. 12. 13.
Sketch the figure and find its area.
14. A square with side lengths of 2.2 centimeters
15. A rectangle with a base of 4 meters and a height of 11 meters
16. A rectangle with a base of 13 feet and a height of 8 feet
Visualize It!
5 m
12.1 m
7 yd
6 yd
2 cm
5 cm
20 in.
12 m
6 ft
Practice and Applications
x
2x
x
2x
Skill Check
Vocabulary Check
Guided Practice
Example 1: Exs. 8–10, 14
Example 2: Exs. 11–13,
15, 16
Example 3: Exs. 20–22
Example 4: Exs. 24–26
Example 5: Exs. 27–30
Homework Help
2
3
6
6
3
B
A
C
7
Page 4 of 6
428 Chapter 8 Polygons and Area
Judo
The dimensions of the squares on a judo mat are given in
the diagram.
17. Find the area of the entire mat.
18. Find the area of the contest area.
19. Find the area of the contest area
including the danger area.
Using Algebra
In Exercises 20–22, A gives the area of the
rectangle. Find the missing side length.
20. 21. 22.
23.
The perimeter of a square is 28 feet. Can
you conclude that the area of the square is 49 square feet? Explain.
Dividing a Polygon
Find the dimensions of the rectangle.
24. Rectangle A
25. Rectangle B
26. Rectangle C
Area of Complex Polygons
Find the area of the polygon made up
of rectangles.
27. 28.
29. 30.
11 cm
12 cm
5 cm
18 cm
4 cm
10 cm
5 yd
7 yd
9 yd
16 yd
3 in.
8 in.
4 in.
5 in.
10 m
5 m
12 m
7 m
You be the Judge
h
6.6 ft
A 5 33 ft
2
b
18 cm
A 5 54 cm
2
h
8 in.
A 5 56 in.
2
4 ft
6 ft
3 ft
2 ft
A
B
C
D
2 ft
2 ft
4 ft
11 ft
Danger
area
Contest
area
14 m
9 m
7 m
In Exs. 27–30, the
polygons can be divided
into rectangles in
different ways. For
example, Ex. 27 can be
divided as follows:
10 m
5 m
12 m
7 m
Visualize It!
Page 5 of 6
8.3 Area of Squares and Rectangles 429
Maize Maze
Brett Herbst transforms cornfields into mazes. His maze
in Utah, shown at the right, is in the shape of Utah.
31. What is the area covered by the maze,
which is made up of two rectangles?
32. How many acres does the maze
cover? (1 acre 5 43,560 square feet)
33. Suppose corn seed costs $34 per
acre and fertilizer costs $57 per acre.
How much will it cost to seed and
fertilize a field with the same
dimensions as the maze?
34.
Multi-Step Problem
The polygon below is made up of rectangles.
a. Write an expression for the area of
the polygon.
b. Suppose the area is 65 square units.
Find the value of x.
c. Using your results from part (b),
sketch the figure and label all of
its dimensions.
Congruent Parts
Use the diagram of parallelogram ABCD. Match
the segment or angle with a congruent one. Give a reason for your
answer.
(Lesson 6.2)
35.
CE&*
A. AB
&*
36. CD
&*
B. aADC
37. aABD C. AE
&*
38. aCBA D. aCDB
Determining Similarity
Determine whether the triangles are similar.
If so, state the similarity and the postulate or theorem that justifies
your answer. (Lesson 7.4)
39. 40.
Comparing Numbers
Compare the two numbers. Write the answer
using <, >, or 5.
(Skills Review, p. 662)
41. 8 and 218 42. 2459 and 2495 43. 210 and 0
44. 21.12 and 21.01 45. 2.44 and 2.044 46. 20.75 and 20.7
Algebra Skills
F G
L
J K
H
10
18
9
8
10
6
P
U
S
R
P
T
1048
1048
25
10
15
6
Mixed Review
Standardized Test
Practice
x
x
7
6
D
E
A
C
B
500 ft 400 ft
175 ft
450 ft
Page 6 of 6