In the parallelogram ABCD on the side AD, a point M is marked such that AM: MD

| April 29, 2021 | education

In the parallelogram ABCD on the side AD, a point M is marked such that AM: MD = 3: 2. Find the area of the triangle ABM if the area of the parallelogram is 60cm ^ 2.

From the vertex B of the parallelogram we draw the height BH, which is simultaneously the height of the triangle ABM and the parallelogram ABCD.

We will use the formula for the area of a parallelogram and express the height of the HV from it.

Savsd = AD * ВН.

ВН = Savsd / AD = 60 / AD. (one).

The area of the triangle ABM will be equal to: Savm = AM * BН / 2.

By condition, AM / MD = 3/2.

3 * MD = 2 * AM.

МD = 2 * AM / 3.

AM = AD – MD.

AM = AD – 2 * AM / 3.

AD = 5 * 3 / AM.

Then AM = 3 * AD / 5. (2).

Substitute expressions 1 and 2 into the formula for the area of a triangle.

Sawm = (3 * AD / 5) * (60 / AD) / 2 = 180/10 = 18 cm2.

Answer: The area of the triangle is 18 cm2.



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