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# A triangle and a parallelogram have the same base and the same area. If the sides of triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram. - CBSE Class 9 - Mathematics

ConceptApplication of Heron’S Formula in Finding Areas of Quadrilaterals

#### Question

A triangle and a parallelogram have the same base and the same area. If the sides of triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.

#### Solution

For triangle

Perimeter of triangle = (26 + 28 + 30) cm = 84 cm

2s = 84 cm

s = 42 cm

By Heron’s formula,

"Area of triangle "=sqrt(s(s-a)(s-b)(s-c))

"Area of triangle "=[sqrt(42(42-26)(42-28)(42-30))]cm^2

=[sqrt(42(16)(14)(12))]cm^2

= 336 cm2

Let the height of the parallelogram be h.

Area of parallelogram = Area of triangle

h × 28 cm = 336 cm2

h = 12 cm

Therefore, the height of the parallelogram is 12 cm.

Is there an error in this question or solution?

#### APPEARS IN

NCERT Solution for Mathematics Class 9 (2018 to Current)
Chapter 12: Heron's Formula
Ex. 12.20 | Q: 4 | Page no. 206

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Solution A triangle and a parallelogram have the same base and the same area. If the sides of triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram. Concept: Application of Heron’S Formula in Finding Areas of Quadrilaterals.
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