Find the area of an isosceles triangle with sides 13cm, 13cm and 10cm.

The area of a triangle is equal to half the product of the height by the length of the side to which this height is drawn. In an isosceles triangle, the height drawn to the base is at the same time the median and divides the base in half. Consider a right-angled triangle in which the hypotenuse is the side, the height to the base and half of the base is the legs. The sum of the squares of the legs is equal to the square of the hypotenuse:
13 ^ 2 = 5 ^ 2 + h ^ 2;
h ^ 2 = 13 ^ 2-5 ^ 2 = 169-25 = 144;
h = √144 = 12.
S = 0.5 * h * 10 = 0.5 * 12 * 10 = 60 cm2.