Transcript Slide 1
9-5 Area of Composite Figures Preview
Holt CA Course 1
9-5 Area of Composite Figures Warm Up Find each area. Round to the nearest tenth, if necessary.
1. a rectangle with length 10 cm and width 4 cm 40 cm 2 2. a parallelogram with base 18 ft and height 12 ft 216 ft 2 3. a triangle with base 16 cm and height 8 cm 64 cm 2 4. a circle with radius 5 in.
78.5 in 2
Holt CA Course 1
9-5 Area of Composite Figures California Standards MG2.2
Estimate and
compute the area of more complex
or irregular
two
-and three-
dimensional figures by breaking the figures down into more basic geometric objects.
Holt CA Course 1
9-5 Area of Composite Figures Additional Example 1A: Finding the Area of Composite Figures by Adding Find the shaded area. Round to the nearest tenth, if necessary.
2 m 8 m 6 m 4 m 2 m 8 m 6 m Divide the figure into a rectangle and a trapezoid.
12 m
area of the rectangle:
A =
b h
A = 12 • 6 A = 72 m 2
Holt CA Course 1
9-5 Area of Composite Figures Additional Example 1A Continued Find the shaded area. Round to the nearest tenth, if necessary.
area of the trapezoid:
2 m 8 m 2 m __
b 1 + b 2 )
4 m 6 m 6 m __ 4 + 2 ) trapezoid.
A = 6 m 2 Add the area of the rectangle and the area of the total area: A = 72 + 6 = 78 m 2 .
Holt CA Course 1
9-5 Area of Composite Figures Additional Example 1B: Finding the Area of Composite Figures by Adding Find the shaded area. Round to the nearest tenth, if necessary.
8 in.
12 in.
20 in.
Divide the figure into a rectangle and a semicircle.
area of the rectangle:
A =
b h
A = 20 • 8 A = 160 in 2
Holt CA Course 1
9-5 Area of Composite Figures Additional Example 1B Continued Find the shaded area. Round to the nearest tenth, if necessary.
8 in.
12 in.
8 in.
area of the semicircle:
__ p
r
2 ) 20 in.
A A
1 2 1 2 ( 3.14
• (50.24) 4 2 )
A
25.1 in 2 Add the area of the rectangle and the area of the semicircle.
total area: A = 160 + 25.1 = 185.1 in 2 .
Holt CA Course 1
9-5 Area of Composite Figures Check It Out!
Example 1A Find the shaded area. Round to the nearest tenth, if necessary.
8 yd Divide the figure into a rectangle and a triangle.
9 yd 10 yd
area of the rectangle:
A =
b h
A = 8 • 9 A = 72 yd 2
Holt CA Course 1
9-5 Area of Composite Figures Check It Out!
Example 1A Continued Find the shaded area. Round to the nearest tenth, if necessary. area of the triangle:
8 yd __
b h
__ 2 • 9 ) 9 yd 10 yd A = 9 yd 2 Add the area of the rectangle and the area of the triangle.
total area: A = 72 + 9 = 81 yd 2
Holt CA Course 1
9-5 Area of Composite Figures Check It Out!
Example 1B Find the shaded area. Round to the nearest tenth, if necessary.
10 m 12 m 22 m 10 m Divide the figure into a rectangle and a semicircle.
area of the rectangle:
A =
b h
A = 22 • 10 A = 220 m 2
Holt CA Course 1
9-5 Area of Composite Figures Check It Out!
Example 1B Continued Find the shaded area. Round to the nearest tenth, if necessary.
12 m 10 m
area of the semicircle:
__ p
r
2 ) 10 m 22 m
A A
1 2 1 2 ( 3.14
(78.5) • 5 2 )
A
39.3 m 2 Add the area of the rectangle and the area of the semicircle.
total area: A = 220 + 39.3 = 259.3 m 2
Holt CA Course 1
9-5 Area of Composite Figures Additional Example 2: Finding the Area of Composite Figures by Subtracting
5 ft
Find the shaded area.
6 ft Subtract the area of the triangle from the area of the rectangle.
12 ft Area of the rectangle: A =
b h
Area of the triangle: __
b h
A = 12 • 9 = 108 ft 2 __ • ( 6 )( 7 ) __ • 42 = 21 ft 2 Shaded area: A = 108 – 21 = 87 ft 2
Holt CA Course 1
9-5 Area of Composite Figures Check It Out!
Example 2 Find the shaded area.
5 in.
Subtract the area of the triangle from the area of the rectangle.
16 in.
9 in.
Area of the rectangle: A =
b h
Area of the triangle: __
b h
A = 16 • 8 = 128 in 2 __ • ( 5 )( 7 ) Shaded area: A = 128 – 17.5 = 110.5 in 2 __ • 35 = 17.5 in 2
Holt CA Course 1
9-5 Area of Composite Figures Additional Example 3: Landscaping Application
6 ft
What is the area of the room floor shown in the figure? Round to the nearest tenth.
12 ft 12 ft 6 ft 18 ft To find the area, divide the composite figure into a square, a rectangle, and a semicircle.
Holt CA Course 1
9-5 Area of Composite Figures Additional Example 3 Continued
6 ft Area of the square: 12 ft A =
s 2
A = 6 2 = 36 ft 2 12 ft 18 ft Area of the rectangle: A =
b h
A = 18 • 6 = 108 ft 2 Area of the semicircle: p
r 2 A A
1 2 • 3.14
• ( __ 2 (254.34) 127.17 ft 2 9 ) 2 6 ft
Holt CA Course 1
9-5 Area of Composite Figures Additional Example 3 Continued
6 ft
What is the area of the room floor shown in the figure? Round to the nearest tenth.
12 ft 12 ft 18 ft Area of the room: A = 36 + 108 + 127.17 = 271.17 ft 2 The area of the room is approximately 271.2 ft 2 .
6 ft
Holt CA Course 1
9-5 Area of Composite Figures Check It Out!
Example 3
5 ft
What is the area of the stage floor shown in the figure? Round to the nearest tenth.
10 ft 10 ft 15 ft 5 ft To find the area, divide the composite figure into a square, a rectangle, and a semicircle.
Holt CA Course 1
9-5 Area of Composite Figures Check It Out!
Example 3 Continued
5 ft Area of the square: 10 ft A =
s 2
10 ft A = 5 2 = 25 ft 2 15 ft Area of the rectangle: A =
b h
A = 15 • 5 = 75 ft 2 Area of the semicircle: p
r
2
A A
1 2 • 3.14
• ( 7.5
2 ) __ 2 (314) 88.3 ft 2 5 ft
Holt CA Course 1
9-5 Area of Composite Figures Check It Out!
Example 3 Continued
5 ft
What is the area of the room floor shown in the figure? Round to the nearest tenth.
10 ft 10 ft 15 ft Area of the room: A = 25 + 75 + 88.3 = 188.3 ft 2 The area of the room is 188.3 ft 2 .
5 ft
Holt CA Course 1
9-5 Area of Composite Figures Lesson Quiz: Part l Find the perimeter and area of each figure. Round to the nearest tenth, if necessary.
1.
3.
5 ft 111 ft 2 45.9 in 2
2.
188.9 mm 2
Holt CA Course 1
9-5 Area of Composite Figures Lesson Quiz: Part ll
4. The figure gives the dimensions of a backdrop for a school play. Find the area of the backdrop.
97 ft 2
Holt CA Course 1