SOLUTION: In trapezoid ABCD, AB || CD. Let P be the midpoint of AD. If the area of triangle APB is 5, and the area of triangle CDP is 17,then find the area of trapezoid ABCD.

Algebra ->  Surface-area -> SOLUTION: In trapezoid ABCD, AB || CD. Let P be the midpoint of AD. If the area of triangle APB is 5, and the area of triangle CDP is 17,then find the area of trapezoid ABCD.       Log On


   

Question 1150783: In trapezoid ABCD, AB || CD. Let P be the midpoint of AD. If the area of triangle APB is 5, and the area of triangle CDP is 17,then find the area of trapezoid ABCD.
Answer by greenestamps(13200) About Me  (Show Source):
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Let Q be the midpoint of BC, so that PQ is the midsegment of the trapezoid.

Let AB=2x and CD=2y; and let the height of the trapezoid be 2h.

Then the altitudes of triangles ABP and CDP are both h.

The area of triangle ABP is one-half base times height: %281%2F2%29%282x%29%28h%29+=+xh+=+5

The area of triangle CDP is one-half base times height: %281%2F2%29%282y%29%28h%29+=+yh+=+17

The area of the trapezoid is the average of the bases times the height:

ANSWER: The area of the trapezoid is 44