Area of rectangle 10 by 6 with a triangle cut out base 4 height 3 Step by Step

Step by step

The question

Question: find the area of this shape: a 10 by 6 rectangle with a triangle cut out, base 4 and height 3.

1 The whole and the hole

The whole shape would be a 10 by 6 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.

10 times 6 is 60.

whole = 10 × 6 = 60

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

hole = 12 × 4 × 3

Careful!

A triangle is half of the box around it.

So we take half of 12.

Careful: not 4 × 3 = 12 ✗

4 times 3 is 12.

hole = 12 × 12

Half of 12 means 12 divided by 2.

That is 6.

122 = 6

So the hole is 6 square units.

hole = 6

3 Take away the hole

The area is the whole, take away the hole.

A = 60 − 6

60 minus 6 is 54.

So the area is 54 square units.

A = 54

4 Check

Let's check: put the triangle back.

We should get the whole rectangle.

54 + 6 = 60

We get 60, 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.

Answer