In an isosceles triangle, the side is 13 cm, the base is 10 cm. Find the area of the triangle.

Let ABC be an isosceles triangle with the base of the AC, let’s draw the height of the ВН.

1). In an isosceles triangle, the height drawn to the base is the median, which means:

AH = HC = AC / 2 = 5 (cm)

2). The AВН triangle is rectangular. We find the ВН by the Pythagorean theorem:

BH = (AB ^ 2 – AH ^ 2) ^ (1/2) = (13 ^ 2 – 5 ^ 2) ^ (1/2) = (169 – 25) ^ (1/2) = 144 ^ (1 / 2) = 12 (cm)

3). Let’s find the area of the triangle ABC:

S = 1/2 * AC * ВН = 1/2 * 10 * 12 = 60 (sq. Cm)

Answer: the area of the triangle is 60 sq. Cm.