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Question

# Find the area of a parallelogram ABCD in which AB=3 cm, BC=7 cm and AC=8 cm using Heron's formula.

A

6 cm2

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B

12 cm2

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C

18 cm2

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D

24 cm2

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Solution

## The correct option is B 12 cm2 Since, ABCD is a parallelogram, its opposite sides will be equal. ⇒CD=AB=3 cm and AD=BC=7 cm Now in triangle ABC, Calculating area of the triangle using heron’s formula, s=Perimeter2=AB+BC+AC2=3+7+82=9 cm ⇒ Area =√s(s−a)(s−b)(s−c) =√9(9−3)(9−7)(9−8) =√9×6×2×1 =6√3 cm2 Now, area of the parallelogram =2× Area of triangle ABC ⇒ The area of the parallelogram =2×6√3=12√3 cm2

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