KEY CONCEPTS
A composite figure is made up of more than one simple
shape.
To determine the total area of a composite figure, add and/or
subtract areas.
To determine the perimeter of a composite figure, add the
distances around the outside of the figure.
EXAMPLE 1
Area and Perimeter of a Composite
Figure
l 25 cm
w
16 cm
h
Calculate the area and perimeter for
the composite figure shown
AREA
We need to calculate the area of each
shape
ATRIANGLE
bh

2
(12)(16)
2
192

2

 96cm 2
ARECTANGLE  lw
 (25)(16)
12 cm
b
AHALF CIRCLE 
 400cm 2
Total area
= 96 + 400 + 100.48
= 596.48 cm2

r 2
2
 (8) 2
2
64

2

200.96
2
This is
diameter (d)
r=d/2
= 16 / 2
= 8 cm
 100.48 cm 2
EXAMPLE 1
Area and Perimeter of a Composite
Figure
Calculate the area and perimeter for
the composite figure shown
25 cm
20 cm
b
16 cm
PERIMETER
We need to add up the
lengths/distances of all the sides
12 cm
a
Use Pythagorean Theorem to solve for
length of hypotenuse
c 2  a 2  b2
c 2  (12) 2  (16) 2
c 2  144  256
c 2  400
c 2  400
c  20
This is
diameter (d)
r=d/2
= 16 / 2
= 8 cm
EXAMPLE 1
Area and Perimeter of a Composite
Figure
Calculate the area and perimeter for
the composite figure shown
25 cm
20 cm
16 cm
b
PERIMETER
We need to add up the
lengths/distances of all the sides
25 cm This is
diameter (d)
r=d/2
= 16 / 2
= 8 cm
12 cm
a
Perimeter
= 12 + 20 + 25 + 25.12 + 25
= 107.12 cm
Distance around circle = circumference
2r
2
2 (8)

2
CHALF CIRCLE 

50.24
2
 25.12 cm
EXAMPLE 2
Area and Perimeter of a Composite
Figure (Part 2)
Calculate the area and perimeter for
the object pictured
(a)
w
8.2 cm
Explain how you would solve
for the area of the shape
pictured?
Calculate the area of the
rectangle
Subtract the area of the
half-circle
(b)
This is
diameter (d)
r=d/2
= 5.8 / 2
= 2.9 cm
Calculate the area
Total area
= 47.56 – 13.20
= 34.36 cm2
ARECTANGLE  lw
 (5.8)(8.2)
 47.56 cm 2
AHALF CIRCLE 
r 2
2
 (2.9) 2

2
5.8 cm
l
8.41
2
26.41

2

 13.20 cm 2
EXAMPLE 2
Area and Perimeter of a Composite
Figure (Part 2)
Calculate the area and perimeter for
the object pictured
(c)
This is
diameter (d)
r=d/2
8.2 cm
= 5.8 / 2
= 2.9 cm
Calculate the perimeter
First, we need to find the circumference of the
half-circle
2r
2
2 (2.9)

2
18.21

2
 9.11cm
CHALF CIRCLE 
9.11 cm
w
8.2 cm
5.8 cm
l
Total perimeter
= 5.8 + 8.2 + 9.11 + 8.2
= 31.31 cm
Homework:
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