In an isosceles triangle, the side is 25 cm, and the height drawn to the base is 24 cm. Find the area of this triangle.

1) Because ABC is isosceles, then AB = BC = 25cm, AC is the base, BH = 24cm, etc. ВН is the height drawn to the base, then ВН is both the median and the bisector.
2) Consider a triangle ABН – rectangular, AB = 25cm, BH = 24cm.
By the Pythagorean theorem AB2 = BH2 + AH2
means AH2 = AB2 – BH2
AH2 = 25 * 25 – 24 * 24
AH2 = 625 – 576
AH2 = 49
AH = 7cm
3) Because. ВН – median, then НС = АН = 7cm, then АС = АН + НС = 7 + 7 = 14cm.
4) Because. ABC is a triangle, then S = ½ * ВН * AC
S = ½ * 24 * 14
S = 168cm2
Answer: 168cm2