In trapezoid abcd with legs ab and cd , diagonals bd ∩ ac =m so that bm: md=1: 4. find aamd, acmd, and aacd if the area of aabm=8 in2.

Area of triangle AMD is 32 square inches.

Area of triangle CMD is 8 square inches.

Area of triangle ACD is 40 square inches.

Step-by-step explanation:

In trapezoid ABCD with legs AB and CD.

Diagonal BD and AC intersect at M so that BM:MD=1:4

We are given ar(ABM)=8 in²

Ratio of area of two triangle is equal to ratio of their base.

Thus, Area of triangle AMD is 32 square inches.

If two triangles lie on same base and same parallel line then their area is equal.

Thus, Area of triangle ACD is 40 square inches.

Thus, Area of triangle CMD is 8 square inches.

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