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Question

The adjacent sides of a parallelogram ABCD measure 34 cm and 20 cm, and the diagonal AC measures 42 cm. Find the area of the parallelogram.

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Solution

Let ABCD is a parallelogram;
AD =20cm
CD =34 cm
and AC = 42 cm
in ΔADC;
s= 34+20+42 = 48;

As per Heron's formula area of triangle = s(sa)(sb)(sc)

Area of Δ ADC = 48(4842)(4834)(4820)

Area of Δ ADC = 48×6×14×28

Area of Δ ADC =336 cm²

Area of parallelogram = 2 × area of Δ ADC

= 672 cm²


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