Step by step
The question
Question: find the area of this shape: a 10 by 4 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 10 by 4.
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: 4.
2 Area of each part
The rectangle: length times width.
10 times 4 is 40.
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.
4² means 4 times 4.
That is 16.
So it is a quarter of π times 16.
A quarter of 16 means 16 divided by 4.
That is 4.
We write it as 4π.
3 Add the parts
The whole area is the two parts added: 40 + 4π.
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.
4 times 3.14 is 12.56.
40 plus 12.56 is 52.56.
So the area is about 52.56 square units.
5 Check
Let's check it makes sense.
The whole shape fits in a box 14 by 4: 56.
Let's check it makes sense.
The area must be more than the rectangle alone: 40.
And less than the box: 56.
52.56 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.