Chapter 8.2 Perimeter and Area of Composite Figures

- Many shapes seen everyday are made up of several different simple shapes (such as triangles and squares)

- A composite figure is a shape made up of different simple shapes

- To find the area of a composite figure, it is required to first split the shape up into several smaller simple shapes

Ex.

 

In this example, we can split the composite figure into three different shapes: a semi-circle, a rectangle, and a right triangle.

Using the formulas, A=lw, A=(bh)/2, A=(Πr²)/2 , find the area of the composite figure.

 

For the semi-circle: A=(Πr²)/2 For the rectangle: A=lw

A=(Π(2.5 cm)²)/2 A=(10cm)(5cm)

A=(Π x 6.25)/2 A=50cm²

A=(19.63495375)/2

A=9.817476875 cm²

For the triangle:

A=(bh)/2

A=(3cm x 5cm)/2

A=15/2

A=7.5 cm²

 

Total Area:

A=9.817476875 cm²+50cm²+7.5 cm²

A=67.317476875cm² rounded to: 67.3 cm²

 

-Using the measurements given, we can also easily find the perimeter of the composite figure

Ex.For Semi-circle: C=Πd For hypotenuse:a²+b²=c²

C=Π(5 cm) 5²+3²=c²

C=15.707963 cm 25+9=c²

34=c²

c=5.831 cm

P= 15.707963cm + 10cm + 13cm+ 5.831cm

P=44.538963cm

rounded to: 44.5 cm