In the KMPT parallelogram the diagonal MT is perpendicular to the side MK, MK-13cm

univerkov | April 9, 2021 | education

In the KMPT parallelogram the diagonal MT is perpendicular to the side MK, MK-13cm, M T5 cm, M P-14cm. Find the area of the parallelogram and its height.

When diagonal MT is drawn, two equal triangles are formed – MKT and MTP.

By condition, the triangle MKT has a right angle, therefore, it is right-angled.

S (MKT) = 0.5 * MT * KM = 0.5 * 5 * 13 = 32.5 cm ^ 2.

Then S (KMPT) = 2 * S (MKT) = 65 cm ^ 2.

h1 = S / a1 = 65/13 = 5 cm.

h2 = S / a2 = 65/14 = 4 9/14 cm.

Answer: 65 cm ^ 2; 5 cm; 4 9/14 cm.

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