In an isosceles triangle, the side is 13 cm, and the height drawn to the base is 5 cm. Find the area of this triangle.

In order to find the area of a triangle, you need to multiply the height by the base:
S = a * h.
To do this, you need to calculate the length of the base of this triangle.
Take, for example, the triangle ABN formed by the height. Using the Pythagorean theorem, you can find the segment AH, which is half the base:
AB2 = BH2 + AH2;
AH2 = AB2 – BH2;
AH2 = 132 – 52 = 169 – 25 = 144;
AH = √144 = 12 cm.
AC = 2 * AН;
AC = 2 * 12 = 24 cm.
S = AC * BH;
S = 24 * 5 = 120 cm2.
Answer: the area of this triangle is 120 cm2.