The perimeter of an isosceles triangle = 162 °, and the base = 32 cm Find the area of a triangle.

In an isosceles triangle, the sides are equal to each other and equal to half the difference between the perimeter and the length of the base:

b = (162 – 32) / 2 = 130/2 = 65 cm – side.

The height drawn to the base of the isosceles triangle is the median and bisects the base. This height, side and half of the base form a right-angled triangle. By the Pythagorean theorem, we can write:

h ^ 2 = b ^ 2 – (a / 2) ^ 2 = 65 ^ 2 – (32/2) ^ 2 = 4225 – 256 = 3969;

h = √3969 = 63 cm.

The area of ​​a given triangle can be found as half the product of the base and the height drawn to this base:

S = 0.5 * h * a = 0.5 * 63 * 32 = 1008 cm2.