The side of an isosceles triangle is 25 and the base is 14. Find the area of this triangle.

Given:
Treug.ABC
AB = AC = 25
BC = 14
To find:
S treug. ABC
Decision:
Consider triug. ABC
Draw from point A the height (AH) to the base BC
Since ABC is an isosceles triangle, the height in it is the median
Means
BH = HC
Consider a triangle AHC
angle H = 90 degrees
HC = BC / 2 = 14/2 = 7
AC = 25
By the Pythagorean theorem, we find AH ^ 2 = (AC ^ 2-HC ^ 2) = 625-49 = 576
AH = root of 576 = 24
Consider a triangle ABC
S treug. ABC = Height (AH) * Base (BC) / 2 = 24 * 14/2 = 168
Answer: 168