Step by step
The question
Question: find the area of a 6 square with a quarter circle cut out of one corner.
1 The whole and the hole
The whole shape would be a 6 square.
A quarter circle is cut out of one corner.
That part is not there any more.
So we take it away.
Its center is the corner of the square.
Its radius is the side of the square: 6.
2 Area of each part
The whole square: side times side.
6 times 6 is 36.
The quarter circle is a quarter of a circle.
A circle is π times r squared.
So we take a quarter.
Careful!
A quarter circle is one quarter of a circle, not one half.
Four of them make a whole circle.
6² means 6 times 6.
That is 36.
So it is a quarter of π times 36.
A quarter of 36 means 36 divided by 4.
That is 9.
We write it as 9π.
3 Take away the hole
The area is the whole, take away the quarter circle: 36 − 9π.
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.
9 times 3.14 is 28.26.
36 minus 28.26 is 7.74.
So the area is about 7.74 square units.
5 Check
Let's check: put the quarter circle back.
That is about 28.26.
We should get the whole square.
We get 36, the whole square.
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.