10-3
10-3Area
AreaofofComposite
CompositeFigures
Figures
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
11
10-3 Area of Composite Figures
Warm Up
1. What is the area of a rectangle with
length 10 cm and width 4 cm? 40 cm2
2. What is the area of a parallelogram with
base 18 ft and height 12 ft? 216 ft2
3. What is the area of a triangle with base
16 cm and height 8 cm? 64 cm2
Course 1
10-3 Area of Composite Figures
Problem of the Day
Four squares are stacked in a tower. The
bottom square is 12 inches on a side. The
perimeter of each of the other squares is
half of the one below it. What is the
perimeter of the combined figure?
69 in.
Course 1
10-3 Area of Composite Figures
Learn to break a polygon into simpler
parts to find its area.
Course 1
10-3 Area of Composite Figures
Additional Example 1A: Finding Areas of
Composite Figures
Find the area of the polygon.
1.7 cm
1.3 cm
4.9 cm
2.1 cm
Think: Break the polygon apart into
rectangles.
Find the area of each rectangle.
Course 1
10-3 Area of Composite Figures
Additional Example 1A Continued
1.7 cm
1.3 cm
4.9 cm
2.1 cm
A = lw
A = lw
A = 4.9 • 1.7
A = 8.33
A = 2.1
•
A = 2.73
Write the formula
1.3 for the area of a
rectangle.
8.33 + 2.73 = 11.06
Add to find the total area.
The area of the polygon is 11.06 cm2.
Course 1
10-3 Area of Composite Figures
Additional Example 1B: Finding Areas of
Composite Figures
Find the area of the polygon.
Think: Break the figure apart into a
rectangle and a triangle.
Find the area of each polygon.
Course 1
10-3 Area of Composite Figures
Additional Example 1B Continued
A = lw
A = 28 • 24
A = 672
672 + 168 = 840
1
__
A = bh
2
1
__
A=
• 28
2
A = 168
12
Add to find the total area
of the polygon.
The area of the polygon is 840 ft2.
Course 1
•
10-3 Area of Composite Figures
Check It Out: Example 1A
Find the area of the polygon.
1.9 cm
5.5 cm
1.9 cm
1.5 cm
5.5 cm
2 cm
3.4 cm
Think: Break the polygon apart into
rectangles.
Find the area of each rectangle.
Course 1
1.5 cm
2 cm
10-3 Area of Composite Figures
Check It Out: Example 1A Continued
1.9 cm
5.5 cm
1.5 cm
2 cm
A = lw
A = lw
A = 5.5 • 1.9
A = 10.45
A=2
A=3
•
1.5
Write the formula
for the area of a
rectangle.
10.45 + 3 = 13.45
Add to find the total area.
The area of the polygon is 13.45 cm2.
Course 1
10-3 Area of Composite Figures
Check It Out: Example 1B
Find the area of the polygon.
20 ft
16 ft
22 ft
36 ft
22 ft
20 ft
22 ft
Think: Break the figure apart into a
rectangle and a triangle.
Find the area of each polygon.
Course 1
10-3 Area of Composite Figures
Check It Out: Example 1B Continued
20 ft
22 ft
A = lw
A = 22 • 20
A = 440
440 + 176 = 616
16 ft
22 ft
1
__
A = bh
2
1
__
A=
• 22
2
A = 176
16
Add to find the total area
of the polygon.
The area of the polygon is 616 ft2.
Course 1
•
10-3 Area of Composite Figures
Additional 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
25
l = 5, w = 5; A = 5 • 5 = 25
Rectangle 2
l = 10, w = 5; A = 10 • 5 = 50
Rectangle 3
l = 15, w = 5; A = 15 • 5 = 75
Rectangle 4
l = 20, w = 5; A = 20 • 5 = 100
Course 1
20
15
10
5
0
5
10 15 20
25
10-3 Area of Composite Figures
Additional Example 2 Continued
Add the areas of the four rectangles to find
the total area of the design.
25 + 50 + 75 + 100 = 250 square units.
The area of the design is 250 square units.
Course 1
10-3 Area of Composite Figures
Helpful Hint
You can also count the squares and multiply by
the area of one square. 1 square = 25 square
units. 10 • 25 = 250 square units.
Course 1
10-3 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
25
20
1
15
Rectangle 2
l = 5, w = 15; A = 5 • 15 = 75
Rectangle 3
l = 5, w = 10; A = 5 • 10 = 50
Course 1
2
10
3
5
0
5
10 15 20
25
10-3 Area of Composite Figures
Check It Out: Example 2 Continued
Add the areas of the three rectangles to find
the total area of the design.
50 + 75 + 50 = 175 square units.
The area of the design is 175 square units.
Course 1
10-3 Area of Composite Figures
Lesson Quiz
1. Find the area of the figure shown.
220 units2
2. Phillip designed a countertop.
Use the coordinate grid to
find its area.
30 units2
Course 1