SOLUTION: I guess this question would be under Geometry- I couldn't tell. My daughter has to find the perimeter, and then the area (two different questions) and show her work for a figure

Question 45325: I guess this question would be under Geometry- I couldn't tell.
My daughter has to find the perimeter, and then the area (two different questions) and show her work for a figure that is 6 feet on three sides, then the fourth side has an arc with "3" written in bold. I don't know if I showed her right on the perimeter- but would it be 6ft. time 3 sides, plus 9 more feet for a total perimeter of 27 feet? If that is right, how would we show that? Also, I know how to find area, but how do you do that with the arc or semi circle attached to the square? Thank you!
Answer by tutmath(14) (Show Source):
You can put this solution on YOUR website!
From your description of the problem, I am assuming the figure has 3 equal sides with 6 ft each and if the fourth side were completed it would have formed a square but instead there is an arc (semi-circle).
Perimeter:
For the arc, we will need to use the formula for the perimeter of a circle that is = 2 * pi * r and divide it by 2
where pi = 22/7 = 3.1428
and r = radius of the circle, in this case it is 3 ft
Thus the perimeter of the arc is 3.1428 * 3 = 9.4284
So the total perimeter = 6 times 3 + 9.4284 = 27.4284 ft

Area:
The total area of the figure will be the Area of the Square + Area of the semicircle
Area of square = 6 * 6 = 36 square ft
Area of circle = pi * r^2
Area of the semi-circle is area of circle divided by 2
Thus, area of the arc/semi-circle = 3.1428 * 3 * 3 / 2 = 14.1426 square ft.
Total area = 36 + 14.1426 = 50.1426 sq. ft
(If you have any questions about this solution you can ask me at tutmath@gmail.com)