Area of L shape 10 by 8 cut 4.5 by 3 Step by Step

Step by step

The question

Question: find the area of this L-shape: 10 by 8, with a 4.5 by 3 corner cut out.

1 Split into rectangles

This shape is not a rectangle.

One line cuts it into two rectangles.

We call them top and bottom.

2 Find the missing sides

The top side is the whole 10, take away the 4.5 cut out.

10 minus 4.5 is 5.5.

10 − 4.5 = 5.5

The right side is the whole 8, take away the 3 cut out.

8 minus 3 is 5.

8 − 3 = 5

3 Area of each part

The top rectangle is 5.5 by 3.

top = 5.5 × 3 = 16.5

Forget the points: 55 times 3 is 165.

The numbers have 1 digit after the point.

So the answer has 1 too: 16.5.

55 × 3 = 165 → 16.5

The bottom rectangle is 10 by 5.

10 times 5 is 50.

bottom = 10 × 5 = 50

4 Add the parts

The whole area is the two parts added.

A = 16.5 + 50

16.5 plus 50 is 66.5.

So the area is 66.5 square units.

A = 66.5

5 Check

Let's check another way: the whole 10 by 8 rectangle, take away the corner.

10 × 8 − 4.5 × 3 = 80 − 13.5 = 66.5

We get 66.5 again.

So the area is right!

Let's look back.

First: split into rectangles.

Then: find the missing sides.

Then: area of each part.

Then: add the parts.

Last: check.

Answer