Question 260303
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