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Question

Two adjacent sides of a parallelogram are 51cm and 37cm. One of its diagonals is 20cm, then its area is:


A

412 cm2

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B

512 cm2

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C

612 cm2

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D

712 cm2

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Solution

The correct option is C

612 cm2


Let ABCD be the given parallelogram as shown above.

Diagonal of a parallelogram divides it into two triangles of equal areas.

Hence, area (parallelogram ABCD) =2 area (ΔBCD)

Let us calculate the area of ΔBCD by using Heron’s Formula.

s=51+37+202=1082=54

Area of ΔBCD

=54(5451)(5437)(5420)

=54×3×17×34

=3 × 3 × 3 × 2 ×3×17×17 × 2

= 17 × 2 × 3 × 3 =306 cm2

So, area of parallelogram ABCD =2×306 cm2=612 cm2


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