Find the area of an isosceles triangle with a base of 10 cm and a side of 13 cm.

1. Vertices of the triangle – A, B, C. AC = 10 centimeters. AB = 13 centimeters. ВH – height. S is the area of the triangle.

2. The segment AH = 1/2 AC, since the height of the BH in an isosceles triangle also performs the functions of the median and divides the side to which it is drawn into two identical segments:

AH = AC: 2 = 10: 2 = 5 centimeters.

3. ВН = √АВ² – АН² (by the Pythagorean theorem).

BH = √AB² – AH² = √13² – 5² = √169 – 25 = √144 = 12 centimeters.

3. S = AC / 2 x BH = 10: 2 x 12 = 60 centimeters².