SOLUTION: I am having trouble figuring out part C of this problem: A farm has the shape of a rectangle with an equilateral triangle on one end of the rectangle and a semicircle on the opp

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Question 984669: I am having trouble figuring out part C of this problem:
A farm has the shape of a rectangle with an equilateral triangle on one end of the rectangle and a semicircle on the opposite end of the rectangle. The length of the rectangle is three times the radius of the semicircle.
a.) Write a function for the perimeter of the farm in terms of the radius of the semicircle.
b.) Write a function for the area of the farm in terms of the radius of the semicircle.
c.) Write a function for the area of the farm in terms of the perimeter of the farm.
Thank you!
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
length of rectangle (l) = 3 * r where r is the radius of the semicircle
width of rectangle (w) = 2 * r
side of triangle (s) = 2 * r
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a) Perimeter (P) = circumference of semicircle + (2 * length of rectangle) + (2 * side of triangle)
P = (pi * r) + (2 * 3 * r) + (4 * r) = r * (pi + 10) = 13.14 * r
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b) Area (A) = (1/2) * Area of circle + Area of rectangle + area of equilateral triangle
A = ((1/2) * pi * r^2) + (2 * r * 3 * r) + ((1/2) * (2 * r) * r*square root(3))
A = r^2 * ( (pi/2) + 6 + (square root(3)) = 9.30 * r^2
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c) A = P * r - 3.84
note that pi is 3.14