Composite Shapes
Math 10-3
Ch.3 Measurement

Consider a rectangle with the dimensions
2 cm by 3 cm.

-What is the perimeter?
= 10 cm

-What is the area? Arectangle = l x w = 3 x 2
= 6 cm2
2+3+2+3
Let’s now increase the dimensions by a
factor of two.
 The new dimensions are 4 cm by 6 cm

-What is the perimeter? 6 + 4 + 6 + 4 =
20 cm
 -What is the area?
lxw=6x4=
24 cm2

Let’s increase the dimensions one more
time by two
 The new dimensions are now 8 cm by 12
cm

What is the perimeter? 12 + 8 + 12 + 8 =
40 cm
 What is the area?
l x w = 12 x 8
=
96 cm2

Let’s now put this information in a
chart:
Rectangle
Length
Width
Perimeter
Area
Original
(#1)
Original
dimension
s x 2 (#2)
3 cm
2 cm
10 cm
6 cm2
6 cm
4 cm
20 cm
24 cm2
Rectangle
#2
dimension
x 2 (#3)
12 cm
8 cm
40 cm
96 cm2

Can you see a pattern forming for the total
perimeter of the rectangle?


Can you see a pattern forming for the area of the
rectangle?



The new perimeter is the old perimeter x 2
The new area is the old area x 4 OR x 22
If you can’t see the pattern, try dividing the area
of rectangle #3 by the area of rectangle #2
96  24 = 4

Could you predict the perimeter and area
for the next rectangle?
Perimeter = 40 cm x 2 = 80 cm
 Area = 96 cm2 x 4 = 384 cm2


We would say that by increasing the
dimensions by two, it increase the
perimeter by a factor of 2 and the area
by a factor of 4 or by 22 !
Composite Shapes

A Composite shape is a shape that is
made up of 2 or more polygons.

We can use what we already know about
perimeter and area to calculate the total
perimeter and area of composite shapes.
Ex1. What is the perimeter and area of
the following composite shape?
Calculate the perimeter first….
*Remember, perimeter is the total
length AROUND THE OUTSIDE of a
shape.

P = 8 + 4.5 + 3 + 3 + 4.5 = 23 cm
Now calculate the area….

The area will be a little trickier to
calculate. To help, visualize what shapes
make up the composite shape.
Triangle
Rectangle
Now, calculate the area of each shape
separately
What is the length of the base of the
triangle?

We can see from the composite solid that
the base of the triangle is the same length
as the longest side of the rectangle, 8 cm
Area
1
 Atriangle =
2
bh =
1
2
x 8 cm x 5 cm = 8 x 5 2
=20 cm2

Arectangle = l x w = 8 x 4.5 cm
= 36 cm2

The TOTAL area will be these two areas added
together: 20 cm2 + 36 cm2 = 56 cm2