On the AB side of the parallelogram ABCD, point M was marked.

univerkov | September 29, 2021 | education

On the AB side of the parallelogram ABCD, point M was marked. Find the area of the parallelogram if the area of the triangle MCD is 38

The segments CM and CD divide the parallelogram into three triangles.

Height DH for triangles ADM and CBM is common.

Sadm = AM * DH / 2.

Svcm = BM * DH / 2.

Then Sadm + Svsm = DH * (AM + BM) / 2 = DH * AB / 2.

The heights DH and MK are equal, since they are drawn to parallel sides, then

Smsd = CD * MK / 2 = DH * AB / 2 = Sadm + Svcm.

Then Savsd = 2 * Smsd = 2 * 38 = 76 cm2.

Answer: The area of the parallelogram is 76 cm2.

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