Step by step
The question
Question: find the area of a 10 cm square with a quarter circle cut out of one corner.
1 The whole and the hole
The whole shape would be a 10 cm 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: 10 cm.
2 Area of each part
The whole square: side times side.
10 times 10 is 100.
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.
10² means 10 times 10.
That is 100.
So it is a quarter of π times 100.
A quarter of 100 means 100 divided by 4.
That is 25.
We write it as 25π.
3 Take away the hole
The area is the whole, take away the quarter circle: 100 − 25π.
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.
25 times 3.14 is 78.5.
100 minus 78.5 is 21.5.
So the area is about 21.5 cm².
5 Check
Let's check: put the quarter circle back.
That is about 78.5.
We should get the whole square.
We get 100, 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.