The adjacent sides of a parallelogram are 21 cm and 28 cm. If its one diagonal is 35 cm, find the area of the parallelogram.

Let the parallelogram be ABCD as shown in the figure below:

For triangle ABC,

AB = 21 cm, BC = 28 cm and AC = 35 cm.

$∵ s = \dfrac{a + b + c}{2}\\[1em] = \dfrac{21 + 28 + 35}{2}\\[1em] = \dfrac{84}{2}\\[1em] = 42$

∵ Area of triangle ABC = $\sqrt{s(s - a)(s - b)(s - c)}$

= $\sqrt{42(42 - 21)(42 - 28)(42 - 35)}$ cm²

= $\sqrt{42 \times 21 \times 14 \times 7}$ cm²

= $\sqrt{86,436}$ cm²

= 294 cm²

∵ Diagonal of parallelogram divides it into two equal parts.

So, area of parallelogram ABCD = 2 x area of triangle ABC.

= 2 x 294 cm²

= 588 cm²

Hence, the area of the parallelogram is 588 cm².