Area of Composite Shapes
We are learning to…find the area of
composite shapes (shapes made up of more
than one figure).

Area of Composite Shapes
Example #1: Find the area of the composite shape below.
10 feet
4 feet
Plan:
Area of a Rectangle + Area of ½ Circle
l(w) + ½ πr
2
4(10) + ½ π(2)
2
Diameter = 4 feet
Radius = 2 feet
4(10) + ½ π(4)
40 + ½ π(4)
40 + (1.57)(4)
40 + 6.28
46.28 square feet

Area of Composite Shapes
Example #2: Find the area of the shaded region.
Plan:
Area of a Square - Area of Circle
l(w) - πr
2
4(4) - π(2)
2
4(4) - π(4)
16 - π(4)
16 - 12.56
3.44 square cm
4 cm
4 cm
4 cm
4 cm

Area of Composite Shapes
Example #3: Find the area of the shaded region.
Plan:
Area of a Trapezoid - Area of a Triangle
½(h)(b1 + b2) - ½(b)(h)
½(4)(18) - ½(6)(4)
6 in
5 in
4 in
12 in
½(4)(6 + 12) - ½(6)(4)
36 - ½(6)(4)
36 - 12
24 square inches

Area of Composite Shapes
Example #4: Find the area of the shaded region.
Plan:
Area of a Trapezoid - Area of a Circle
½(h)(b1 + b2) - πr
2
½(8)(21) - π(4)
2
½(8)(6 + 15) - π(4)
2
½(8)(21) - π(16)
84 - π(16)
33.76 square feet
8 ft
15 ft
6 ft
10 ft
84 – 50.24

Area of Composite Shapes
Example #5: Find the area of the polygon below.
Plan:
Area of a Rectangle+ Area of a Rectangle
l(w)+ l(w)
162 + 55
9(18) + 5(11)
217 Square inches
18
in
5
in
11 inches
9 inches