Lunar Eclipse: Umbra and penumbra radii

1. The problem statement, all variables and given/known data
Find the radii of the umbra and penumbra circles drawn drawn perpendicular to the EMS axis, formed at a distance equal to that of the moon from the Earth.

2. Relevant equations
(From: http://ift.tt/1iWvvkX)

D2 / L1 = (P + U) / (L1 + L2)
D1 / L1 = P / L2
Total Shadow = 2P + U

D1 = Diameter of light source
D2 = Diameter of object between light source and Shadow
L1 = Length from light source to L1
L2 = Length from L1 to Umbra
U = Umbra
P = Penumbra

3. The attempt at a solution
I substituted 12,576 km for D2 as the diameter of earth and 149.6 million km for the distance between the earth and sun. My calculations revealed that P+U= 1305010.784. Am I misguided in the belief that these equations give my the area of the circles from which I can extrapolate the radii?

http://ift.tt/1iWvvl1

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