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.
It is given that the parallelogram and triangle have equal areas.
The sides of the triangle are given as 26 cm, 28 cm and 30 cm.
So, the perimeter = 26 + 28 + 30
= 84 cm
And its semi perimeter = 84/2 cm
= 42 cm
Now, by using Heron’s formula,
area of the triangle
= \(\sqrt{s(s - a)(s - b)(s - c)}\)
= \(\sqrt{42(42 - 26)(42 - 28)(42 - 30)}\)cm2
= \(\sqrt{42 \times 16 \times 14 \times 12}\)cm2
= 336 cm2
Now, let the height of parallelogram be h.
As the area of parallelogram = area of the triangle
28 cm× h = 336 cm2
∴ h = 336/28 cm
So, the height of the parallelogram is 12 cm.