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.
Plan:
Area of a Rectangle + Area of ½ Circle
2
l(w) + ½ πr
4 feet
2
4(10) + ½ π(2)
10 feet
4(10) + ½ π(4)
Diameter = 4 feet
40 + ½ π(4)
Radius = 2 feet
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
2
l(w) - πr
4 cm
4 cm
2
4 cm
4(4) - π(2)
4(4) - π(4)
16 - π(4)
4 cm
16 - 12.56
3.44 square cm
Area of Composite Shapes
Example #3: Find the area of the shaded region.
Plan:
Area of a Trapezoid - Area of a Triangle
6 in
½(h)(b1 + b2) - ½(b)(h)
½(4)(6 + 12) - ½(6)(4)
4 in
5 in
½(4)(18) - ½(6)(4)
36 - ½(6)(4)
36 - 12
24 square inches
12 in
Area of Composite Shapes
Example #4: Find the area of the shaded region.
15 ft
Plan:
Area of a Trapezoid - Area of a Circle
2
½(h)(b1 + b2) - πr
10 ft
8 ft
2
½(8)(6 + 15) - π(4)
2
½(8)(21) - π(4)
½(8)(21) - π(16)
6 ft
84 - π(16)
84 – 50.24
33.76 square feet
Area of Composite Shapes
Example #5: Find the area of the polygon below.
Plan:
9 inches
Area of a Rectangle + Area of a Rectangle
l(w) + l(w)
18
in
9(18) + 5(11)
162 + 55
217 Square inches
11 inches
5
in