Composite Shapes

Math 10-3Ch.3 Measurement

Consider a rectangle with the dimensions 2 cm by 3 cm.

-What is the perimeter? 2 + 3 + 2 + 3 = 10 cm

-What is the area? Arectangle = l x w = 3 x 2 = 6 cm2

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? l x w = 6 x 4 = 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)

3 cm 2 cm 10 cm 6 cm2

Original dimensions x 2 (#2)

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? The new perimeter is the old perimeter x 2

Can you see a pattern forming for the area of the rectangle? 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 separatelyWhat 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 Atriangle = bh = 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

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