The perimeter of an isosceles triangle is 36 and the base is 16. Find the area of the triangle.

From the condition it is known that the perimeter of an isosceles triangle is 36 cm, and it is also known that its base is 16 cm. In order to find the length of the lateral side, we compose and solve the equation.

But first of all, let’s remember how to find the perimeter of an isosceles triangle.

In general, the sum of the lengths of all sides of the triangle is called the perimeter. But in an isosceles triangle, the sides are equal to each other.

The perimeter can be written as.

P = 2a + b, where a is the side and b is the base of the triangle.

2a + 16 = 36;

2a = 36-16;

2a = 20;

a = 20: 2;

a = 10 cm side length.

We look for the area according to Heron’s formula:

S = √p (p – a) (p – b) (p – c), p = 36/2 = 18 cm.

S = √18 (18 – 10) (18 – 10) (18 – 16) = √18 * 8 * 8 * 2 = 8 * 6 = 48 cm2