Step by step
The question
Question: find the area of this shape: an 8 by 4 rectangle with a semicircle on the long side.
1 Split into parts
This shape is made of simple shapes.
A dashed line splits off the round top.
The rectangle is 8 by 4.
The round top is a semicircle: half of a circle.
2 Area of each part
The rectangle: length times width.
8 times 4 is 32.
The semicircle sits on the long side of the rectangle.
So its diameter is 8.
The radius is half of it: 8 divided by 2 is 4.
Careful!
The semicircle sits on the long side, 8.
Its radius is half of 8, not half of 4.
The semicircle is half of a circle.
A circle is π times r squared.
So we take half.
4² means 4 times 4.
That is 16.
So it is half of π times 16.
Half of 16 is 8.
We write it as 8π.
3 Add the parts
The whole area is the two parts added: 32 + 8π.
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.
8 times 3.14 is 25.12.
32 plus 25.12 is 57.12.
So the area is about 57.12 square units.
5 Check
Let's check it makes sense.
The whole shape fits in a box 8 by 8: 64.
Let's check it makes sense.
The area must be more than the rectangle alone: 32.
And less than the box: 64.
57.12 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.