Transcript Area of Squares and Rectangles

Area of Squares and
Rectangles
Section 8.3
Goal
• Find the area of squares and rectangles.
Key Vocabulary
• Area
• Square
• Rectangle
Definition: Area
• Area is the amount of space inside a
figure. We use square units to
describe area.
What Is Area ?
Area is the amount of space inside a shape:
Area
Area
Area
Area
Area
Area
Area
Area
Area
Area
Area
Area
Area
Area
Area
Area
Area
Area
Area
Area
Area is measured in square units.
1unit2
A square unit is a square measuring
one unit in each direction.
1unit
It is written as:
1unit2
1unit
Area of
Rectangles and Squares
The area of a closed figure is the number of
square units contained in the figure.
4 units
2 units
Area of
Rectangles and Squares
What is the area of the rectangle? In other
words, how many unit squares are
contained within the rectangle?
Area of
Rectangles and Squares
Notice that finding the area of a rectangle is
exactly the same as using a multiplication
table.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
2
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
3
3
6
9
12
15
18
21
24
27
30
33
36
39
42
45
4
4
8
12
16
20
24
28
32
36
40
44
48
52
56
60
5
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
6
6
12
18
24
30
36
42
48
54
60
66
72
78
84
90
7
7
14
21
28
35
42
49
56
63
70
77
84
91
98
105
Area of
Rectangles and Squares
Bases and Heights
Any one of the sides of a
rectangle can be
considered a base. A
rectangle’s height is the
length of the side that is
perpendicular to the base.
Area of a Rectangle
• The area of a rectangle is
the product of its base and
height.
• Words:
Area = (base)(height)
• Symbols: A = bh
Area of a Square
• For squares, the formula is still
A=bh. However, since every
side of a square is the same,
then it can also be expressed
as A=s2 where s equals the
length of one side.
• Words: Area = (side)2
• Symbols: A = s2
Example 1
Find the Area of a Square
Find the area of the square.
SOLUTION
Use the formula for the area of a square and substitute
9 for s.
A = s2
Formula for the area of a square
= 92
Substitute 9 for s.
= 81
Simplify.
ANSWER
The area of the square is 81 square feet.
Example 2
Find the 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 = bh
Formula for the area of a rectangle
= 24 · 16
Substitute 24 for b and 16 for h.
= 384
Multiply.
ANSWER
The area of the pool is 384 square feet.
Example 3
Find the Height 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 = bh
54 = 9h
6=h
ANSWER
Formula for the area of a rectangle
Substitute 54 for A and 9 for b.
Divide each side by 9.
The height of the rectangle is 6 inches.
Your Turn:
Find the area of the quadrilateral.
1.
2.
3.
ANSWER
121 m2
ANSWER
12 ft2
ANSWER
26.55 yd2
4. A rectangle has an area of 52 square meters and a
height of 4 meters. Find the length of its base.
ANSWER
13 m
Dividing Complex Polygons into
Rectangles
Find the area of this figure. All angles are right angles. Dimensions
are in centimeters.
Use formulas.
2
5
A1
4
A2
2
AT
AT
AT
AT
 A1  A2
 b1h1  b2 h2
 5 2   4 2
 10  8
AT  18 cm2
Dividing Complex Polygons into
Rectangles
Find the area of the shaded portion of this figure. All angles are
right angles. Dimensions are in meters.
Use formulas.
AS  A1  A2
6
A2
2
8
10
A1
AS  b1h1  b2 h2
AS  108   6 2
AS  80  12
AS  68 m 2
Example 4
Divide a Complex Polygon into 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 = 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 – 5 = 4 units.
Example 5
Find the Area of a Complex Polygon
Find the area of the polygon made up
of rectangles.
SOLUTION
Add the areas of the rectangles.
Area = Area of F + Area of G + Area of H
= bh + bh + bh
= 4 · 3 + (7 – 4) · (9 – 2) + 5 · 2
=4·3+3·7+5·2
= 12 + 21 + 10
= 43
ANSWER
The total area of the polygon is 43
square centimeters.
Your Turn:
Find the area of the polygon made up of rectangles.
1.
ANSWER
30 in.2
ANSWER
54 m2
2.
Assignment:
• Pg. 427 – 429: # 1 – 9 all, 11 – 29 odd