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Question

Find the area of a parallelogram ABCD in which AB = 28 cm, BC = 26 cm and diagonal AC = 30 cm.

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Solution

Let: a=26 cm, b =30 cm and c=28 cms= a+b+c2=26+30+282=42 cmBy Heron's formula, we have:Area of triangle ABC = s(s-a)(s-b)(s-c)=42(42-26)(42-30)(42-28)=42×16×12×14=14×3×4×4×2×2×3×14=14×4×2×3=336 cm2

We know that a diagonal divides a parallelogram into two triangles of equal areas.
∴ Area of parallelogram ABCD = 2(Area of triangle ABC) = 2×336=672 cm2

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