Composite Figures – Area and Perimeter

Key Concepts

• Composite Figures
• Area and perimeter of composite figures 

Prior Knowledge:  

Find the missing sides a and b of the given figure and calculate its perimeter. 

Answer: 

We get the length of side a  by adding together the ones opposite it: 3 and 6. 

a = 3 cm + 6 cm = 9 cm 

Now, we need to subtract 7 from 10 to get side b. 

b = 10 cm – 7 cm = 3 cm 

Perimeter = 10 + 3 + 3 + 6 + 7 + 9 = 38 cm. 

13.2 Composite Figures 

Definition: 

A composite shape or a composite figure is a shape that is made up of two or more common shapes. 

The area of the composite shapes is the area of combined shapes of one, or more simple polygons and circles. 

There are two general methods for finding the area of a composite shape. 

Method 1: Find the individual areas of each piece of the composite shape. The area of the composite shape will be the sum of the individual areas. 

Method 2: Find the area of a shape larger than the composite shape and the areas of the pieces of the larger shape that is not included in the composite shape. The area of the composite shape will be the difference between the area of the larger shape, and the areas of the pieces of the larger shape not included in the composite shape. 

Example 1: 

Calculate the area and the perimeter of the following shape. 

The composite shape is made up of a rectangle and a triangle. 

Area = area of a rectangle + area of a triangle 

          = length × breadth +

12

× base × height 

For the rectangle: 

Length = 16 cm, width = 12 cm 

For triangle: 

Base = 12 cm (same as width of rectangle) 

Height = (24 – 16) = 8 cm 

So, area = 16 × 12 +

12

  × 12 × 8  

  = 192 + 48 

  = 240 cm² 

Perimeter = sum of the lengths of 5 sides 

       = 16 + 10 + 10 + 16 + 12 

       = 64 cm 

Exercise:

1. A rectangular window has a length of 7 centimeters and a width of 4 centimeters. Find
   the perimeter of the rectangular window.
2. What is the area of the given shape?

3. A rectangular balcony has an area of 45 square feet and a perimeter of 28 feet. What are
   the dimensions of the balcony?
4. A rectangular deck has an area of 192 square feet. Its perimeter is 56 feet. What are the
   dimensions of the deck?
5. A photograph is 6 inches wide and 10 inches tall with each opposite side being
   congruent. A frame shop charges $1.00 per inch for a silver frame. How much would it
   cost to buy a silver frame for the photograph?
6. The sides of a square-shaped room measures 9 feet. Stephanie wants to buy carpet to
   cover the floor of the room. If the carpet costs $3.00 per square foot, how much will it
   costto buy carpet for the room?
7. Emily wants to purchase new carpet for her rectangular living room. The room is 14 feet
   wide and 18 feet long. There is also a rectangular fireplace that is 3 feet wide and 5 long
   that takes up a portion of the room, Carpet costs $3.00 per square foot. How much would
   it cost Emily to carpet the room?
8. Deanna’s backyard needs a new fence. The backyard is 10 yards long and 8 yards wide
   with each opposite side being congruent. It costs $3.50 per yard to install a fence. How
   much would it cost Deanna to install a new fence?
9. The area of rectangular envelope is 60 square inches. Its perimeter is 34 inches. What
   are the dimensions of the envelope?
10. Daniel needs to paint the base area of his L-shaped pool. Dimensions of the pool are
    given in the figure below. What is the total area of Daniel’s pool that will be painted?

What have we learnt :

Understand the meaning of composite figures
Solve composite figures by dividing them into two figures
Solve word problems involving estimating area of figures
Solve word problems involving area and perimeter of composite figures

Concept Map: 

Perimeter of different shapes formulas: