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Question:

A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26cm, 28cm and 30cm and the parallelogram stands on the base 28cm, find the height of the parallelogram.

Solution:

Perimeter of Triangle
2S=26+28+30=84⇒S=42cm
Area√s(s−a)(s−b)(s−c)(Heron's formula)
Area=√42(42−26)(42−28)(42−30)=√42×16×14×12
Area=336cm2
Area of parallelogram=Area of triangle⇒h×28=336⇒h=12cm
Height of parallelogram=12cm