A triangle and a parallelogram have same base and same area. If the sides of the triangle are 20cm,25cm and 35cm, and the base side is 25 cm for the triangle as well as the parallelogram, find the vertical height of the parallelogram.
Area of triangle =√s(s−a)(s−b)(s−c).
For triangle with sides 20 cm, 25 cm and 35 cm, s=20+25+352=40cm
Area of the triangle =√40(40−20)(40−25)(40−35)
=√40×20×15×5
=√20×2×20×5×3×5
=20×5×√6
=100√6cm2
Given, area of the parallelogram = Area of the triangle =100√6cm2
Area of a parallelogram =base×height.
So 25×height=100√6
=>height=4√6cm