Area of rectangle 10 m by 8 m with a circle radius 2 cut out Step by Step

Step by step

The question

Question: find the area of this shape: a 10 m by 8 m rectangle with a circle of radius 2 m cut out.

1 The whole and the hole

The whole shape would be a 10 m by 8 m rectangle.

A circle is cut out.

That part is not there any more.

So we take it away.

2 Area of each part

The whole rectangle: length times width.

10 times 8 is 80.

whole = 10 × 8 = 80 m²

The hole is a circle: π times r squared.

hole = π × 2²

2² means 2 times 2.

That is 4.

2² = 2 × 2 = 4

π times 4 is written 4π.

hole = 4π m²

3 Take away the hole

The area is the whole, take away the hole: 80 − 4π.

We keep π in the answer.

That is the exact answer.

A = 80 − 4π m²

4 About how much

To see about how much, put 3.14 for π.

A ≈ 80 − 4 × 3.14

4 times 3.14 is 12.56.

A ≈ 80 − 12.56

80 minus 12.56 is 67.44.

So the area is about 67.44 m².

A ≈ 67.44 m²

5 Check

Let's check: put the hole back.

That is about 12.56.

We should get the whole rectangle.

67.44 + 12.56 = 80

We get 80, the whole rectangle.

So the area is right!

Let's look back.

First: the whole and the hole.

Then: area of each part.

Then: take away the hole.

Then: about how much.

Last: check.

Answer