SOLUTION: https://imgur.com/8J0Mleu ABCD is a trapezoid with AD ||BC. If AD = 5 cm and BC = 11 cm, and if the area of the trapezoid is 80 cm^2, find the area of triangle ABE, in cm^2.

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: https://imgur.com/8J0Mleu ABCD is a trapezoid with AD ||BC. If AD = 5 cm and BC = 11 cm, and if the area of the trapezoid is 80 cm^2, find the area of triangle ABE, in cm^2.      Log On

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Question 1187826: https://imgur.com/8J0Mleu ABCD is a trapezoid with AD ||BC. If AD = 5 cm and BC = 11 cm, and if the area of the trapezoid is 80 cm^2, find the area of triangle ABE, in cm^2.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

With AD parallel to BC and E the midpoint of CD, the area of triangle ABE is half the area of the trapezoid.
ANSWER: The area of triangle ABE is 166cm%5E2%2F2+=+83cm%5E2.
To see that this is true, consider the midline EF of the trapezoid.
Let the height of the trapezoid be 2x; then the altitudes of triangles ADE,+AFE, BFE, and BEC are all+x.

The area of triangle ABE is the sum of the areas of triangles AFE and BFE:
%281%2F2%29%2811%29%28x%29%2B%281%2F2%29%2811%29%28x%29+=+11x
The area of the trapezoid is
%281%2F2%29%288%2B14%29%282x%29+=+22x
So the area of triangle ABE is half+the area of the trapezoid.