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# Geometry Trapezoid

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What is the area of right trapezoid ABCD if AD= 8 and BC =12? (The diagonals are perpendicular. I've been stuck on this for a while now, and have no clue on how to solve it.

Jan 15, 2019

#1
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Since the trapezoid is orthodiagonal or right, we have $$a=\frac{8+12}{2}=10,$$ where $$a$$ is the altitude. Thus, the area is 100.

Jan 15, 2019
#3
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Thanks!

But, can you prove that fomula? I want to understand it

itsyaboi  Jan 15, 2019
#2
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i suppose you can set B as (0, 0), put the whole thing on a coordinate plane, and solve it that way by setting DC's length as x.

HOPE THIS *hint* HELPED!

Jan 15, 2019
#4
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Remember, when a trapezoid is orthodiagonal, meaning having a 90 degrees angle; a right trapezoid, the sum of the two bases divided by 2 is the altitude. In this case, we have the two bases as 8 and 12, so $$\frac{8+12}{2}=10$$ and by using the formula for the area of a trapezoid, we get $$\frac{1}{2}*20*10=\boxed{100}.$$

Hope this helped!  Jan 15, 2019