Step by step
The question
Question: find the area of this shape: a 14 by 8 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 14 by 8.
The round top is a semicircle: half of a circle.
2 Area of each part
The rectangle: length times width.
14 times 8 is 112.
The semicircle sits on the long side of the rectangle.
So its diameter is 14.
The radius is half of it: 14 divided by 2 is 7.
Careful!
The semicircle sits on the long side, 14.
Its radius is half of 14, not half of 8.
The semicircle is half of a circle.
A circle is π times r squared.
So we take half.
7² means 7 times 7.
That is 49.
So it is half of π times 49.
Half of 49 is 24.5.
We write it as 24.5π.
3 Add the parts
The whole area is the two parts added: 112 + 24.5π.
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.
Forget the points: 245 times 314 is 76930.
Together, the numbers have 1 + 2 = 3 digits after the point.
So the answer has 3 too: 76.930, which is 76.93.
So we have 112 + 76.93.
112 plus 76.93 is 188.93.
So the area is about 188.93 square units.
5 Check
Let's check it makes sense.
The whole shape fits in a box 14 by 15: 210.
Let's check it makes sense.
The area must be more than the rectangle alone: 112.
And less than the box: 210.
188.93 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.