8-5 area of composite figures learn to break a polygon into simpler parts to find its area
TRANSCRIPT
8-5 Area of Composite Figures
Learn to break a polygon into simpler parts to find its area.
8-5 Area of Composite FiguresAdditional Example 1A: Finding Areas of Composite
Figures
Find the area of the polygon.
Think: Break the polygon apart into rectangles.
Find the area of each rectangle.
1.7 cm
4.9 cm 1.3 cm
2.1 cm
8-5 Area of Composite FiguresAdditional Example 1A Continued
A = lw A = lw
A = 4.9 • 1.7 A = 2.1 • 1.3Write the formula for the area of a rectangle.A = 8.33 A = 2.73
8.33 + 2.73 = 11.06 Add to find the total area.
The area of the polygon is 11.06 cm2.
1.7 cm
4.9 cm
1.3 cm
2.1 cm
8-5 Area of Composite Figures
Think: Break the figure apart into a rectangle and a triangle.
Find the area of each polygon.
Additional Example 1B: Finding Areas of Composite Figures
Find the area of the polygon.
8-5 Area of Composite FiguresAdditional Example 1B Continued
A = lw
A = 28 • 24
A = 672 A = 168
672 + 168 = 840 Add to find the total area of the polygon.
The area of the polygon is 840 ft2.
A = bh12__
A = • 28 • 1212__
8-5 Area of Composite FiguresCheck It Out: Example 1A
Find the area of the polygon.
Think: Break the polygon apart into rectangles.
Find the area of each rectangle.
1.9 cm
1.5 cm
2 cm
3.4 cm
5.5 cm
1.9 cm
5.5 cm 1.5 cm
2 cm
8-5 Area of Composite Figures
A = lw A = lw
A = 5.5 • 1.9 A = 2 • 1.5Write the formula for the area of a rectangle.A = 10.45 A = 3
10.45 + 3 = 13.45 Add to find the total area.
The area of the polygon is 13.45 cm2.
Check It Out: Example 1A Continued
1.9 cm
5.5 cm 1.5 cm
2 cm
8-5 Area of Composite FiguresCheck It Out: Example 1B
Find the area of the polygon.
Think: Break the figure apart into a rectangle and a triangle.
Find the area of each polygon.
36 ft
22 ft
20 ft
20 ft
22 ft
22 ft
16 ft
8-5 Area of Composite Figures
A = lw
A = 22 • 20
A = 440 A = 176
440 + 176 = 616 Add to find the total area of the polygon.
The area of the polygon is 616 ft2.
A = bh12__
A = • 22 • 1612__
Check It Out: Example 1B Continued
20 ft22 ft
22 ft
16 ft
8-5 Area of Composite FiguresAdditional Example 2: Art Application
Patrick made a design. Use the coordinate grid to find its area.
Think: Divide the design into rectangles. Find the area of each rectangle.Rectangle 1
l = 5, w = 5; A = 5 • 5 = 25
Rectangle 2l = 10, w = 5; A = 10 • 5 = 50
Rectangle 3l = 15, w = 5; A = 15 • 5 = 75
Rectangle 4l = 20, w = 5; A = 20 • 5 = 100
0
10
15
20
5 10
5
15 20 25
25
8-5 Area of Composite FiguresAdditional Example 2 Continued
25 + 50 + 75 + 100 = 250 square units.
Add the areas of the four rectangles to find the total area of the design.
The area of the design is 250 square units.
8-5 Area of Composite Figures
You can also count the squares and multiply by the area of one square. 1 square = 25 square units. 10 • 25 = 250 square units.
Helpful Hint
8-5 Area of Composite Figures
Check It Out: Example 2
Lawanda made a design. Use the coordinate grid to find its area.
Think: Divide the design into rectangles. Find the area of each rectangle.
Rectangle 1
l = 5, w = 10; A = 5 • 10 = 50
Rectangle 2l = 5, w = 15; A = 5 • 15 = 75
Rectangle 3l = 5, w = 10; A = 5 • 10 = 50
0
10
15
20
5 10
5
15 20 25
3
2
1
25
8-5 Area of Composite Figures
Check It Out: Example 2 Continued
50 + 75 + 50 = 175 square units.
Add the areas of the three rectangles to find the total area of the design.
The area of the design is 175 square units.