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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
avatar+4582 
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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
avatar+4582 
+1

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! smileysmiley

 Jan 15, 2019

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