Step by step
The question
Question: find the area of this shape: an 8 by 4 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 8 by 4.
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.
8 times 4 is 32.
Each semicircle sits on an end of the rectangle.
So its diameter is 4.
The radius is half of it: 4 divided by 2 is 2.
The two semicircles make one circle: π times r squared.
2² means 2 times 2.
That is 4.
π times 4 is written 4π.
3 Add the parts
The whole area is the two parts added: 32 + 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.
32 plus 12.56 is 44.56.
So the area is about 44.56 square units.
5 Check
Let's check it makes sense.
The whole shape fits in a box 12 by 4: 48.
The area must be more than the rectangle alone: 32.
And less than the box: 48.
44.56 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.