Question

Find the area of a triangle whose sides are 9cm and 5cm and perimeter is 21cm

Answer 1

First, find the third side. Since perimeter is the sum of sides, we have 9+5+x = 21.

14 + x = 21 or x = 7cm.

Now, using Heron's formula, we can find the area as given below (since this is a scalene triangle, with all three sides unequal).

Area = sqrt (s*(s-a)*(s-b)*(s-c))

where s = semi-perimeter.

Thus, s = 21/2 = 10.5.

Area = sqrt (10.5 * (10.5-5) * (10.5 - 9) * (10.5-7))
         = sqrt (10.5 * 5.5 * 1.5 * 3.5)
         = sqrt (303.1875)
         = 17.41228 sq. cm.

Thus, the area of the triangle is 17.41228 sq. cm.