Question

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

Answer 1

First we find area of $\Delta ABC.$

Sides are, a=28 cm

b =35 cm

and c =21 cm

$S=\frac{a+b+c}{2}$

$=\frac{28+35+21}{2}$

$=\frac{84}{2}=42cm$

area of $\Delta ABD=\sqrt{S(S-a)(S-b)(S-c)}$

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

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

$=\sqrt{2\times 21\times 2\times 7\times 7\times 21}$

$=\sqrt{2\times 2\times 21\times 21\times 7\times 7}$

$=2\times 21\times 7$

$=294c{m}^2$

$\because$ Diagonal of ||gm divides it into two equal parts.

$\therefore$ area of ||gm $=2\times$ area of $\Delta ABC$

$=2\times 294=588c{m}^2$