Question

The adjacent sides of a parallelogram measures 34 m, 20 m and the measure of the diagonal is 42 m. Find the area of parallelogram

Answer 1

Since ABCD is a parallelogram opposite sides are equal.

In the ΔABC

a = 20 m, b = 42 m and c = 34 m

s = `("a" + "b" + "c")/2`

= `(20 + 42 + 34)/2  "cm"`

= `96/2`

= 48 m

s – a = 48 – 20 = 28 m

s – b = 48 – 42 = 6 m

s – c = 48 – 34 = 14 m

Area of the ΔABC

= `sqrt("s"("s" - "a")("s" - "b")("s" - "c"))`

= `sqrt(48 xx 28 xx 6 xx 14)`

= `sqrt(2^4 xx 3 xx 2^2 xx 7 xx 2 xx 3 xx 2 xx 7)`

= `sqrt(2^8 xx 3^2 xx 7^2)`

= 2⁴ × 3 × 7 sq.m

= 16 × 3 × 7 sq.m

= 336 sq.m

Since ABCD is a parallelogram

Area of ΔABC and Area of ΔACD are equal

Area of the parallelogram ABCD = (336 + 336) sq.m

= 672 sq.m

∴ Area of the parallelogram = 672 sq.m