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.

Answer 1

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 = $\sqrt{s(s-a)(s-b)(s-c)}$

Area of Δ ADC = $\sqrt{48(48-42)(48-34)(48-20)}$

Area of Δ ADC = $\sqrt{48\times 6\times 14\times 28}$

Area of Δ ADC =336 cm²

Area of parallelogram = 2 $\times$ area of Δ ADC

= 672 cm²