Step by step
The question
Question: find the area of this shape: a 20 by 10 rectangle with a semicircle on each end.
1 Split into parts
This shape is made of simple shapes.
Dashed lines split off the round ends.
The rectangle is 20 by 10.
Each round end is a semicircle: half of a circle.
Two halves make one whole circle.
2 Area of each part
The rectangle: length times width.
20 times 10 is 200.
Each semicircle sits on an end of the rectangle.
So its diameter is 10.
The radius is half of it: 10 divided by 2 is 5.
The two semicircles make one circle: π times r squared.
5² means 5 times 5.
That is 25.
π times 25 is written 25π.
3 Add the parts
The whole area is the two parts added: 200 + 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.
200 plus 78.5 is 278.5.
So the area is about 278.5 square units.
5 Check
Let's check it makes sense.
The whole shape fits in a box 30 by 10: 300.
The area must be more than the rectangle alone: 200.
And less than the box: 300.
278.5 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.