Question

Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42cm?

Answer 1

Given: Two sides of the triangle and its perimeter.

By using Heron’s formula, we can calculate the area of triangle.

Heron’s formula for the aera of a triangle is area = `sqrt(s(s-a)(s-b)(s-c))`

Where a, b and c are the sides of the triangle, and s = Semi-perimeter = Half the perimetern of triangle

The sides of triangle given: a = 18 cm, b = 10 cm

Perimeter of the triangle = (a + b + c)

42 = 18 + 10 + c

c = 42 − 28

c = 14 cm

Semi Perimeter

s = (a + b + c) 

= `42/2`

= 21 cm

By using Heron’s formula,

Area of a triangle = `sqrt(s(s-a)(s-b)(s-c))`

= `sqrt(21(21 - 18)(21 - 10)(21 - 14))`

= `sqrt(21(3 xx 11 xx 7)`

= `sqrt(21 xx 3 xx 11 xx 7)`

= `sqrt(441 xx 11)`

= `21sqrt(11)  cm^2`