SOLUTION: ABCD is a trapezoid with AD||BC (AD is parallel to BC). If AD=8cm and BC=14cm, and if the area of the trapezoid is 166cm^2, find the area of triangle ABE, in cm^2. Diagram: htt

Algebra ->  Surface-area -> SOLUTION: ABCD is a trapezoid with AD||BC (AD is parallel to BC). If AD=8cm and BC=14cm, and if the area of the trapezoid is 166cm^2, find the area of triangle ABE, in cm^2. Diagram: htt      Log On


   

Question 1148965: ABCD is a trapezoid with AD||BC (AD is parallel to BC). If AD=8cm and BC=14cm, and if the area of the trapezoid is 166cm^2, find the area of triangle ABE, in cm^2.
Diagram: https://imgur.com/a/4RzEFl1
Answer by greenestamps(13200) 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 166/2 = 83 cm^2.

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.