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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(54−51)(54−37)(54−20) =√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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