Area of square 8 with a triangle on top height 3

Step by step

The question

Question: find the area of this shape: an 8 square with a triangle on top, 3 high.

1 Split into parts

This shape is made of simple shapes.

A dashed line splits it into a rectangle and a triangle.

The square is 8 by 8.

The triangle sits on top.

Its base is the top of the square: 8.

Its height is 3.

2 Area of each part

The square: length times width.

8 times 8 is 64.

The triangle: half of base times height.

8 times 3 is 24.

Half of 24 means 24 divided by 2.

That is 12.

So the triangle is 12 square units.

3 Add the parts

The whole area is the two parts added.

64 plus 12 is 76.

So the area is 76 square units.

4 Check

Let's check another way.

Draw a box around the whole shape: 8 by 11.

Take away the two empty corners.

Each is half of a 4 by 3 box.

So together they are 4 × 3.

We get 76 again.

So the area is right!

Let's look back.

First: split into parts.

Then: area of each part.

Then: add the parts.

Last: check.