Area of rectangle 9 by 7 with a triangle cut out base 5 height 3

Step by step

The question

Question: find the area of this shape: a 9 by 7 rectangle with a triangle cut out, base 5 and height 3.

1 The whole and the hole

The whole shape would be a 9 by 7 rectangle.

A triangle 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.

9 times 7 is 63.

The hole is a triangle: half of base times height.

Careful!

A triangle is half of the box around it.

So we take half of 15.

5 times 3 is 15.

Half of 15 means 15 divided by 2.

That is 7.5.

So the hole is 7.5 square units.

3 Take away the hole

The area is the whole, take away the hole.

63 minus 7.5 is 55.5.

So the area is 55.5 square units.

4 Check

Let's check: put the triangle back.

We should get the whole rectangle.

We get 63, 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.

Last: check.