Question

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

Answer 1

In the figure, ABCD is a parallelogram and ABE is the triangle which stands on the base AB 

For the triangle ABE, a = 30 cm, b = 28 cm, c = 26 cm. 

∴ s = a +b  + c/ 2 =  30 +28+ 26 /2 cm = 42 cm

Now, area of the parallelogram = base × height 

⇒ 336 = 28 × height 

[Given, area of the triangle = area of the parallelogram] 

⇒ Height of the parallelogram = 336/ 28 cm = 12 cm Ans.