A triangle and a parallelogram have the same base and the same area. If the sides of
the triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base
28 cm, find the height of the parallelogram.
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Answer:
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=336cm
2
Area of parallelogram = Area of triangle
⇒ h×28=336
⇒h=12cm
Height of parallelogram =12cm
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