__Question__

What do you call an alligator in a vest?

__Answer__

An investigator of course.

Lets investigate how to find the area of compound shapes including circles.

Compound shapes are shapes made up of two or more simple shapes.

All we need to know is the area of these simple shapes. Lets recap.

Area of a square/rectangle/parallelogram = base x height

Area of a triangle = base x height ÷ 2 OR 1/2 base x height

Area of a circle = π x radius x radius (πr²)

The value of Π is usually taken as 3.14 or use the Π button on your calculator.

Example 1

Here you can separate this shape into a rectangle measuring 9 cm x 8 cm = 72 cm² and a semi circle.

To find the semi circle find the area of the full circle π x 3 x 3 = 28.27 now divide by 2 = 14.14 cm²

Now just add 72 cm² to 14.14 cm² = 86.14 cm²

Example 2

Area of the triangle = 7 x 9 = 63 cm² ÷ 2 = 31.5 cm²

Area of the semi circle = π x 5 x 5 = 78.54 cm² ÷ 2 = 39.27 cm²

Total area = 31.5 cm² + 39.27 cm ² = 70.77 cm²

Your turn to investigate.