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.

# 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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### Solution:

Given that, A triangle and a parallelogram have the same base and the same area

We know that, Heron's formula

Area of triangle =

where, s is the semi-perimeter = half of the perimeter

and  a, b and c are the sides of the triangle

Let ABCD is a parallelogram and ABE is a triangle having a common base with parallelogram ABCD.

For ∆ABE, a = 30 cm, b = 26 cm, c = 28 cm

Semi Perimeter = s  = Perimeter/2

s = (a $+$ b $+$ c)/2

= (30 $+$ 26 $+$ 28)/2

= 84/2

= 42 cm

Thus, we get

Area of a ΔABE =

= 336 cm2

Hence we get,

Area of parallelogram ABCD = Area of ΔABE

Base × Height = 336 cm2

28  × Height = 336 cm2

On rearranging, we get

Height = 336/28 cm = 12 cm

Thus, height of the parallelogram is 12 cm.

## Related content

 Distance Formula Perimeter of Rectangle Area of Square Area of Isosceles Triangle Pythagoras Theorem Triangle Formulae Volume of Cylinder Perimeter of Triangle Formula Area Formulae Volume Formulae

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