A rectangular garden is 10 m by 7 m. A 3 m by 2 m rectangle inside… Step by Step

Step by step

The question

Question: find the area of this shape: a 10 by 7 rectangle with a 3 by 2 hole cut out.

There are four choices.

First we solve it, the normal way.

Then we pick.

1 The whole and the hole

The whole shape would be a 10 by 7 rectangle.

A hole 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 7 is 70.

whole = 10 × 7 = 70

The hole is a 3 by 2 rectangle.

3 times 2 is 6.

hole = 3 × 2 = 6

3 Take away the hole

The area is the whole, take away the hole.

A = 70 − 6

70 minus 6 is 64.

So the area is 64 square units.

A = 64

4 Check

Let's check: put the hole back.

We should get the whole rectangle.

64 + 6 = 70

We get 70, the whole rectangle.

So the area is right!

5 Pick the choice

Our answer is A = 64.

That is choice B.

B) 64

6 Why not the others

A is 6.

Wrong: that is only the pond.

A) 6 ✗ that is only the pond

C is 70.

Wrong: forgot to take the pond away.

C) 70 ✗ forgot to take the pond away

D is 76.

Wrong: added the pond instead of taking it away.

D) 76 ✗ added the pond instead of taking it away

Let's look back.

First: the whole and the hole.

Then: area of each part.

Then: take away the hole.

Then: check.

Then: pick the choice.

Last: why not the others.

Answer