Question

Two adjacent sides of a parallelogram are 28 cm and 26 cm. If one diagonal of it is 30 cm long; find the area of the parallelogram. Also, find the distance between its shorter sides.

Answer 1

At first, we have to calculate the area of the triangle having sides, then its perimeter 28 cm, 26 cm, and 30 cm.

Let a = 28, b = 26, c = 30

S = `[ 28 + 26 + 30 ]/2`

= `84/2`

= 42 cm

By Heron's Formula,

Area of a triangle = `sqrt[s( s - a )( s - b )( s - c )]`

= `sqrt[42( 42 - 28 )( 42 - 26 )( 42 - 30 )]`

= `sqrt( 42 xx 14 xx 16 xx 12)`

= `sqrt( 112896 )`

= 336 cm²

Area of a Parallelogram = 2 × Area of a triangle

= 2 × 336

= 672 cm²

We know that,

Area of a parallelogram = Height × Base

⇒ 672 = Height × 26

⇒ Height = 25.84 cm

∴ The distance between its shorter sides is 25.84 cm.