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

September 15, 2021 | education

| 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.

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