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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.
Solution
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.
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