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In a trapezoid ABCD with AB parallel to CD, the diagonals AC and BD intersect at E. If the area of triangle ABE is 50 units, and the area of triangle ADE is 40 square units, what is the area of trapezoid ABCD?

 Dec 22, 2020
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In a trapezoid ABCD with AB parallel to CD, the diagonals AC and BD intersect at E. If the area of triangle ABE is 50 units, and the area of triangle ADE is 40 square units, what is the area of trapezoid ABCD?

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ABCD quadrilateral is an isosceles trapezoid.

 

Let M and N be the midpoints on AB and CD.

 

Let AB = 20 and EM = 5

 

Angles EAM and EDN are congruent.

 

Let DN be "x"           tan( ∠EDN) = 0.5

 

So, we have              x(0.5 * x) = 40          x = 4√5        CD = 8√5

 

Height        MN = 5 + (0.5 * DN) = 9.472135955

 

[ABCD] = 1/2(AB + CD) * MN ≈ 179.443 u2

 Dec 22, 2020

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