The perimeter of an isosceles triangle is 18 and the base is 8. Find the area of this triangle.

In an isosceles triangle, the sides are equal, we calculate their length:

(18 – 8): 2 = 10: 2 = 5.

We calculate the area of the triangle using Heron’s formula:

S = √ (p (p – a) (p – b) (p – c)), where p is the half perimeter of the triangle, a, b and c are the sides of the triangle.

Find the half-perimeter of the triangle: p = 18: 2 = 9.

Hence S = √ (9 * (9 – 5) (9 – 5) (9 – 8)) = √ (9 * 4 * 4 * 1) = 3 * 4 = 12.

Answer: the area of the triangle is 12.