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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.
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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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