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A parallelogram ABCD has perimeter equal to  124 . Let E be the foot of the perpendicular from A to BC, and let F be the foot of the perpendicular from A to CD. If AE= 7 and AF=20, what is the area of the parallelogram?

 Dec 22, 2021
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I recommend drawing a diagram.

I'm not completely confident about my answer, but here's what I got.

We know that DF+FC+CE+EB = 124/2 = 62, and that 20(DF + FC) = 7(CE + EB), which are just 2 different ways to calculate the area of the parallelogram.

We need to calculate either 20(DF + FC) or 7(CE + EB). 

From our first equation, we get DF + FC = 62 - (CE + EB), so 20(62-(CE+EB)) = 7(CE+EB). Solving, CE+EB = 1240/27 and so the area is 7 * 1240/27 = 8680/27.

 

See https://web2.0calc.com/questions/help-geometry_74

 Dec 22, 2021

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