Find the area of a triangle ABC if ab = 13, bc = 14, ac = 15.

If the lengths of the three sides of the triangle are known, then its area can be found using Heron’s formula:
S = Square root of (p * (p-a) * (p-b) * (p-c)), where p is the semi-perimeter of the triangle, i.e. p = (a + b + c) / 2, a, b, c are the lengths of the sides of the triangle.
Let’s calculate the semi-perimeter:
1) (13 + 14 + 15) / 2 = 42/2 = 21 – semi-perimeter of triangle ABC.
Let’s find the area of the triangle:
2) Square root of (21 * (21-13) * (21-14) * (21-15)) = Square root of (21 * 8 * 7 * 6) = Square root of 7056 = 84 – area of triangle ABC …
Answer: 84.