Step by step
The question
Question: find the area of this shape: a 16 by 12 rectangle with a semicircle cut out of one end.
1 The whole and the hole
The whole shape would be a 16 by 12 rectangle.
A semicircle is cut out of one end.
That part is not there any more.
So we take it away.
2 Area of each part
The whole rectangle: length times width.
16 times 12 is 192.
The semicircle sits on the end of the rectangle.
So its diameter is 12.
The radius is half of it: 12 divided by 2 is 6.
The semicircle is half of a circle.
A circle is π times r squared.
So we take half.
6² means 6 times 6.
That is 36.
So it is half of π times 36.
Half of 36 is 18.
We write it as 18π.
3 Take away the hole
The area is the whole, take away the hole: 192 − 18π.
We keep π in the answer.
That is the exact answer.
4 About how much
To see about how much, put 3.14 for π.
18 times 3.14 is 56.52.
192 minus 56.52 is 135.48.
So the area is about 135.48 square units.
5 Check
Let's check: put the semicircle back.
That is about 56.52.
We should get the whole rectangle.
We get 192, 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.
Then: about how much.
Last: check.