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.

Here, the sides of triangle ABC are a = 28 cm, b = 26 and c = 30 cm.
So, the semi-perimeter of triangle S = a+b+c/2 = 28+26+30+ = 84/2 = 42 cm
Therefore, using Heron’s formula, area of triangle = √s(s – a)(s -b)(s -c)
= √42(42 -28)(42 -26)(42 -30) = √42(14)(16)(12) = √112896
= 366 cm²
We know that the area of a parallelogram = base × corresponting hieght
According to question:
Area of parallelogram = Area of triangle
⇒ base × corresponding height = 336
⇒ 28 × corresponding height = 336
⇒ corresponding height = 336/28 = 12 cm.