Question

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

Answer 1

First, we find the area of ΔABC.

Sides are, a = 28 cm

b = 35 cm

and c = 21 cm

S = `(a + b + c)/2`

= `(28 + 35 + 21)/2`

= `84/2 = 42` cm

area of ΔABD = `sqrt(S(S - a)(S - b)(S - c))`

= `sqrt(42(42 - 28)(42 - 35)(42 - 21))`

= `sqrt(42 xx 14 xx 7 xx 21)`

= `sqrt(2 xx 21 xx 2 xx 7 xx 7 xx 21)`

= `sqrt(2 xx 2 xx 21 xx 21 xx 7 xx 7)`

= `2 xx 21 xx 7`

= 294 cm²

∵ Diagonal of ||gm divides it into two equal parts.

∴ area of ||gm = `2 xx "area of ΔABC"`

= 2 × 294

= 588 cm²