Transcript Area of Composite Shapes

Area of Composite Shapes
We are learning to…find the area of
composite shapes (shapes made up of more
than one figure).
Wednesday, May 6, 2020
Area of Composite Shapes
Review of Important Area Formulas
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Area of a Rectangle:
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Area of a Triangle:
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A = πr2
Area of a Parallelogram:
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A = ½(b)(h)
Area of a Circle:
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A = b(h)
A = b(h)
Area of a Trapezoid:
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A = ½(b1 + b2)h
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
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
2
l(w) - πr
4 cm
4 cm
4 cm
2
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(b1 + b2)(h) - ½(b)(h)
½(6 + 12)(4) - ½(6)(4)
4 in
5 in
½(18)(4) - 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(b1 + b2)(h) - πr
10 ft
8 ft
2
½(6 + 15)(8) - π(4)
2
½(21)(8) - π(4)
½(21)(8) - 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) + lw
18
in
9(13) + 5(20)
18 – 5 =
13 inches
117 + 5(20)
117 + 100
217 Square inches
11 inches
5
in
9 + 11 =
20 inches
Individual Practice
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Try the last example with your team!
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When you are done raise your hand and
show your teacher the solution.