Area of rectangle 10 by 6 with a triangle on top height 4 Step by Step

Step by step

The question

Question: find the area of this shape: a 10 by 6 rectangle with a triangle on top, 4 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 10 by 6.

The triangle sits on top.

Its base is the top of the rectangle: 10.

Its height is 4.

2 Area of each part

The rectangle: length times width.

10 times 6 is 60.

rectangle = 10 × 6 = 60

The triangle: half of base times height.

triangle = 12 × 10 × 4

10 times 4 is 40.

triangle = 12 × 40

Half of 40 means 40 divided by 2.

That is 20.

402 = 20

So the triangle is 20 square units.

triangle = 20

3 Add the parts

The whole area is the two parts added.

A = 60 + 20

60 plus 20 is 80.

So the area is 80 square units.

A = 80

4 Check

Let's check another way.

Draw a box around the whole shape: 10 by 10.

Take away the two empty corners.

Each is half of a 5 by 4 box.

So together they are 5 × 4.

10 × 10 − 5 × 4 = 100 − 20 = 80

We get 80 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.

Answer