Question

Find the area of a triangle whose sides are 27 cm, 45 cm and 36 cm.

Answer 1

Let the sides of a triangle be a = 27cm, b = 45cm and c = 36cm
Semi-perimeter of a tirangle = s

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

= `(27 + 45 + 36)/(2)`
= 54cm
Area of a triangle
= `sqrt("s"("s" - "a")("s" - "b")("s" - "c")`
= `sqrt(54(54 - 27)(54 - 45)(54 - 36)`
= `sqrt(54 xx 27 xx 9 xx 18)`
= `sqrt(6 xx 6 xx 3 xx 9 xx 9 xx 6 xx 3)`
= `sqrt(6 xx 6 xx 3 xx 3 xx 9 xx 9 xx 9)`
= 6 x 3 x 9 x 3
= 486cm².