Calculate the area of an isosceles triangle, the side of which is 13 cm and the base is 10 cm.

The area of a triangle is equal to half the product of the base and the height.

In the problem, we are given an isosceles triangle ABC, where AB = BC = 13 cm are the sides, AC = 10 cm is the base of the triangle.

The height BD, lowered from the top B to the base, divides it into two equal segments:

AD = DC = 10: 2 = 5 cm.

Find the height BD by the Pythagorean theorem:

BD ^ 2 + AD ^ 2 = AB ^ 2 ;.

BD ^ 2 = AB ^ 2 – AD ^ 2;

BD ^ 2 = 13 ^ 2 – 5 ^ 2 = (13 – 5) × (13 + 5) = 8 × 18 = 8 × 2 × 9;

BD = √ (16 × 9);

Find the area of the triangle:

S = ½ × 10 × 12 = 60 cm 2.