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  • The adjacent sides of a parallelogram ABCD are AB = 34 m, BC = 20 m and diagonal AC = 42 m. Thenthe area of the parallelogram is. (in m2)Option: 1</st

The adjacent sides of a parallelogram ABCD are AB = 34 m, BC = 20 m and diagonal AC = 42 m. Thenthe area of the parallelogram is. (in m2)

Option: 1

442


Option: 2

336


Option: 3

574


Option: 4

672


Answers (1)

best_answer

In triangle ABC it is given that

a=B C=20 \mathrm{m}, b=A C=42 \mathrm{m} \text { and } c=A B=34 \mathrm{m}

\begin{aligned} &\begin{array}{l} \therefore \quad s=\frac{1}{2}(20+42+34) \mathrm{m}=48 \mathrm{m} \\ \therefore \quad(s-a)=28 \mathrm{m},(s-b)=6 \mathrm{m} \text { and }(s-c)=14 \mathrm{m} \end{array}\\ &\therefore \quad \text { area of } \triangle A B C=\sqrt{s(s-a)(s-b)(s-c)}\\ &=\sqrt{48 \times 28 \times 6 \times 14} \mathrm{m}^{2}=(14 \times 24) \mathrm{m}^{2}\\ &=336 \mathrm{m}^{2} \end{aligned}

Area of parallelogram = 2 x Area of triangle ABC = 672 m2

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Pankaj

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