Question

. ABCD is a trapezoid with AB parallel to CD. The diagonals AC and BD meet at P . If the area of
ABP is 16 and the area of CDP is 25, what is the area of the trapezoid?

Answer 1

Answer:

Step-by-step explanation:

Triangle CDP is similar to triangle ABP. Because their areas are in the

ratio 1:4, their sides are in the ratio 1:2. In particular AP = 2CP and BP = 2DP.

Because triangles CDP and ADP have the same altitude from D,

Area(ADP) = 2 · Area(CDP) = 2 · 5 = 10.

Similarly, Area(ADP) = 10. Thus the area of trapezoid ABCD = 5 + 10 + 10 + 20 =45   hope u undertand 9

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