Question

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

Answer 1

Area of the parallelogram ABCD $=$ Area of triangle ABD $+$ Area of triangle BCD
Since both the triangles are same, Area of the parallelogram ABCD $=2\times$( Area of triangle ABD)

Area of triangle with sides a, b, and c and s
$=\frac{a+b+c}{2}$ is $\sqrt{s(s-a)(s-b)(s-c)}$.
For triangle with sides 21 cm, 28 cm and 35 cm, $s=\frac{21+28+35}{2}=42cm$

Area of the triangle with sides 21 cm, 28 cm and 35 cm, $=\sqrt{42(42-21)(42-28)(42-35)}=\sqrt{42\times 21\times 14\times 7}=\sqrt{21\times 2\times 21\times 2\times 7\times 7}=21\times 2\times 7=294{cm}^2$

Hence, Area of the parallelogram ABCD $=2\times$( Area of triangle ABD) $=2\times 294=588{cm}^2$