EXPLORING THE AREA OF COMPOSITE SHAPES

A composite shape is made up of several simple geometric shapes such as triangles, rectangles, squares, circles, and semicircles.

The shape given below can be a good example of composite shape. This composite shape is made up of two triangles and one rectangle.  

To find the area of a composite shape, separate the shape into simpler shapes whose area can be found.

Then add the areas together.

Be sure than none of the simpler figures have overlapping areas. 

Exploring Areas of Composite Shapes

Aaron was plotting the shape of his garden on grid paper. While it was an irregular shape, it was perfect for his yard. Each square on the grid represents 1 square meter.

A. Describe one way you can find the area of this garden.

Answer : 

I can divide it into rectangles and triangles, use a formula to find the area of each, and then add the areas together.

B.  Find the area of the garden. 

Answer : 

The area of the garden is 46 square meters.

C.  Compare your results with other students. What other methods were used to find the area?

Answer : 

Other students counted squares; rearranged the triangle to be a rectangle and found the area, and then found the area of the other rectangles in the garden.

D.  How does the area you found compare with the area found using different methods ?

Answer : 

It is the same as the other students.

E.  Use dotted lines to show two different ways Aaron’s garden could be divided up into simple geometric figures.

Answer : 

Finding Areas of Composite Shapes

Find the area of the shape given below. 

Solution :

By drawing a horizontal line (FG)  parallel to the side DC, we can divide the above composite shape into two rectangles.

(i) ABFG is a rectangle

(ii) EGDC is also a rectangle

To get area of the given composite shape, we have to find the area of each rectangle separately and add them. 

Area of ABFG :

Area of rectangle = Length x width

length (AF) = 8 ft and width AB = 5 ft

  =  8 x 5 = 40 square feet ---(1)

Area of EGDC :

length (DC) = 7 ft and width DE = 3 ft

  =  7 x 3 = 21 square feet ---(2)

(1) + (2) : 

Area of the given composite shape is

=  Area of rectangle ABFG + Area of rectangle EGDC

 =  40 + 21

=  61 square feet

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