Area of rectangle 9 by 6 with a triangle on top height 5

Step by step

The question

Question: find the area of this shape: a 9 by 6 rectangle with a triangle on top, 5 high.

1 Split into parts

This shape is made of simple shapes.

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

The rectangle is 9 by 6.

The triangle sits on top.

Its base is the top of the rectangle: 9.

Its height is 5.

2 Area of each part

The rectangle: length times width.

9 times 6 is 54.

The triangle: half of base times height.

9 times 5 is 45.

Half of 45 means 45 divided by 2.

That is 22.5.

So the triangle is 22.5 square units.

3 Add the parts

The whole area is the two parts added.

54 plus 22.5 is 76.5.

So the area is 76.5 square units.

4 Check

Let's check another way.

Draw a box around the whole shape: 9 by 11.

Take away the two empty corners.

Each is half of a 4.5 by 5 box.

So together they are 4.5 × 5.

We get 76.5 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.