Area of rectangle 7.5 by 4 with a triangle on top height 2

Step by step

The question

Question: find the area of this shape: a 7.5 by 4 rectangle with a triangle on top, 2 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 7.5 by 4.

The triangle sits on top.

Its base is the top of the rectangle: 7.5.

Its height is 2.

2 Area of each part

The rectangle: length times width.

Forget the points: 75 times 4 is 300.

The numbers have 1 digit after the point.

So the answer has 1 too: 30.0, which is 30.

The triangle: half of base times height.

Forget the points: 75 times 2 is 150.

The numbers have 1 digit after the point.

So the answer has 1 too: 15.0, which is 15.

So it is half of 15.

Half of 15 means 15 divided by 2.

That is 7.5.

So the triangle is 7.5 square units.

3 Add the parts

The whole area is the two parts added.

30 plus 7.5 is 37.5.

So the area is 37.5 square units.

4 Check

Let's check another way.

Draw a box around the whole shape: 7.5 by 6.

Take away the two empty corners.

Each is half of a 3.75 by 2 box.

So together they are 3.75 × 2.

We get 37.5 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.