Step by step
The question
Question: find the area of this shape: a 12 by 6 rectangle with a quarter circle on the end.
1 Split into parts
This shape is made of simple shapes.
A dashed line splits off the round end.
The rectangle is 12 by 6.
The round end is a quarter circle: a quarter of a circle.
Its center is the corner of the rectangle.
Its radius is the end of the rectangle: 6.
2 Area of each part
The rectangle: length times width.
12 times 6 is 72.
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 Add the parts
The whole area is the two parts added: 72 + 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.
72 plus 28.26 is 100.26.
So the area is about 100.26 square units.
5 Check
Let's check it makes sense.
The whole shape fits in a box 18 by 6: 108.
Let's check it makes sense.
The area must be more than the rectangle alone: 72.
And less than the box: 108.
100.26 is between them.
So the answer makes sense!
Let's look back.
First: split into parts.
Then: area of each part.
Then: add the parts.
Then: about how much.
Last: check.