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.

itsyaboi Jan 15, 2019

#1**0 **

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.

tertre Jan 15, 2019

#2**0 **

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!

asdf335 Jan 15, 2019

#4**+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!

tertre Jan 15, 2019