Geometry Notes
9-3 Composite and Irregular Figures
A composite figure is a shape made up of several different shapes that we can find the area of
(triangles, rectangles, circles, etc.)
To find the area of this, we find the area of each piece and add them together.
Find the area of each shaded figure. Round to the nearest tenth.
Ex. 1:
Semicircle has a radius of 10 mm.
1
1
A = ( πr 2 ) = ( π ⋅102 ) = 50π
2
2
Trapezoid :
 20+ 32 
 52 
A = 14
 = 14  = 14 ⋅ 26 = 364
 2 
 2
Total area : 50π + 364 ≈ 521.1 mm 2
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Parallelogram :
Ex. 2:
A = bh = 8( 5) = 40
Triangle :
1
1
bh = (10)( 5) = 25
2
2
Total area : 40+ 25 = 65 ft 2
A=
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Ex. 3:
Triangle :
1
1
A = bh = (26)(18) = 234
2
2
Semicircle hole has a radius of 4.5 ft :
1
1
A = πr 2 = π (4.5)2 = 10.125π
2
2
Total area : 234 − 10.125π ≈ 202.2 ft 2
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Ex. 4:
Rectangle :
A = bh = 9(4) = 36
Each trapezoid :
 9− 4 
b2 = 
 = 2.5
 2 
 2.5+1 
A = 4
 = 4(1.75) = 7
 2 
Total area : 36+ 7+ 7 = 50 ft 2
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Ex. 5:
Semicircle :
1
1
1
A = πr 2 = π 12 = π
2
2
2
Rectangle :
A = 2(16) = 32
Triangle :
1
1
A = bh = (2)(5) = 5
2
2
1
Total area : π + 32+ 5 ≈ 38.6 cm 2
2
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Ex. 6: Mike is remodeling his kitchen. The countertop he wants costs $2.70 per square foot.
How much will Mike have to spend on his remodeling project?
There are two rectangles that are 2 x 6 ft.
A = bh = 2(6) = 12 ft 2
Total area : 12 +12 = 24 ft 2
Cost : $2.70/ft 2 ⋅ 24 ft 2 = $64.80
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Ex. 7: Use composite figures to estimate the area of the shaded region.
Each square has a side length of 1 cm.
~ 9 cm2
~ 10 cm2
~ 7 cm2
~ 9 cm2