An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.

Explanation

Given: Equal sides of the triangle and its perimeter.
Heron's formula for the area 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 perimeter of the triangle
Equal sides: `a = b = 12 cm` (given)
Perimeter`(P) = a + b + c`
`30 = 12 + 12 + c ` (Given, perimeter `= 30 cm`)
`c = 30 - 24=6 cm`
Now, Semi Perimeter `(s) = P/2 = (a + b + c)/2`
`s = 30/2 = 15 cm`
By using Heron’s formula,
Area of a triangle` = sqrt(s(s - a)(s - b)(s - c))`
`= sqrt((15 - 12)(15 -12)(15 - 6))`
`= sqrt(15 × 3 × 3 × 9)`
`= sqrt(1215)`
`= 9 sqrt(15) cm^2`
Area of the triangle` = 9sqrt(15) cm^2`