SOLUTION: Okay. So how do you find the area of a semi-circle if you already have the perimeter? I am solving a problem where the perimeter is 20 and it wants me to find the area of the semi

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Question 260303: Okay. So how do you find the area of a semi-circle if you already have the perimeter? I am solving a problem where the perimeter is 20 and it wants me to find the area of the semi circle. plz help me out!
Thankss!
Found 3 solutions by Alan3354, drk, edjones:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website!
Find the radius.
The perimeter of a semi-circle = pi*r.
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Then, the area is (1/2)pi*r^2
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Answer by drk(1908)   (Show Source):
You can put this solution on YOUR website!
Lets start with the circumference formula as
(i) C = 2*pi*r
and the area formula as
(ii) A = pi*r^2.
solve the circumference for pi as
(iii) pi = C/(2r)
Now put that into the area formula as
(iv) A = C/(2r)*r^2
which is
(v) A = Cr/2
From (i) the radius is
(vi) r = C/(2pi)
putting (vi) into (v) we get
(vii) A = C^2/(4pi) - - - This is the formula you want.
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You were given perimeter (circumference) = 20
So,
from (vii) we get
A = 20^2/(4pi) = 400/(4pi) = 100/pi

Answer by edjones(8007)   (Show Source):
You can put this solution on YOUR website!
The perimeter of a semi-circle is pi*d/2 + d
The perimeter has 2 parts: the circular part which is 1/2 the circumference of a circle and a flat part which is the diameter of the circle.
pi*d/2 + d=20
pi*d+2d=40
d(pi+2)=40
d=40/(pi+2)
r=20/(pi+2)
.
A=(pi*r^2)/2
=pi*(20/(pi+2))^2/2
=pi*(400/(pi+2)^2)*1/2
=200pi/(pi+2)^2 or 23.77
.
Ed