The side of an isosceles triangle is 17 cm, and the height of the triangle drawn to its base is 15 cm.

The side of an isosceles triangle is 17 cm, and the height of the triangle drawn to its base is 15 cm. Calculate the area of this triangle.

Given:
triangle ABC – isosceles,
AB = BC = 17 centimeters,
ВO – the height drawn to its base AC,
ВO = 15 centimeters.
Find the area of a given triangle ABC, that is, S ABC -?
Decision:
1) Consider the triangle ABC. The height of ВO is also the median, then AO = 1/2 AC;
2) Consider a right-angled triangle ABO. By the Pythagorean theorem:
AO ^ 2 + BO ^ 2 = AB ^ 2;
AO ^ 2 + 15 ^ 2 = 17 ^ 2;
AO ^ 2 = 17 ^ 2 – 15 ^ 2;
AO ^ 2 = 289 – 225;
AO = 64;
AO = 8 centimeters;
3) AC = 8 * 2 = 16 centimeters;
4) S abc = 1/2 * ВO * AC;
S abc = 1/2 * 15 * 16;
S abc = 120 square centimeters.
Answer: 120 square centimeters.