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Question
The adjacent sides of a parallelogram are 21 cm and 28 cm. If it's one diagonal is 35 cm; find the area of the parallelogram.
Solution
First, we find the area of ΔABC.
Sides are, a = 28 cm
b = 35 cm
and c = 21 cm
S = `(a + b + c)/2`
= `(28 + 35 + 21)/2`
= `84/2 = 42` cm
area of ΔABD = `sqrt(S(S - a)(S - b)(S - c))`
= `sqrt(42(42 - 28)(42 - 35)(42 - 21))`
= `sqrt(42 xx 14 xx 7 xx 21)`
= `sqrt(2 xx 21 xx 2 xx 7 xx 7 xx 21)`
= `sqrt(2 xx 2 xx 21 xx 21 xx 7 xx 7)`
= `2 xx 21 xx 7`
= 294 cm2
∵ Diagonal of ||gm divides it into two equal parts.
∴ area of ||gm = `2 xx "area of ΔABC"`
= 2 × 294
= 588 cm2
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