Find the area of a triangle whose medians are 12, 15, and 21.

As you know from the course of mathematics, the area of a triangle can be calculated from three medians using the following formula:

Str = 4/3 * √ (n * (n – ma) * (n – mb) * (n – mc)), n is the half-sum of the indicated medians, and ma; mb and mc, respectively, are the medians themselves.

Let us determine what the half-sum of the medians will equal, which are given in the condition of our problem:

(12 + 21 + 15): 2 = 24.

Let’s determine what the area will be equal to:

4/3 * √ (24 * (24 – 12) * (24 – 15) * (24 – 21)) = 4/3 * √ (24 * 12 * 9 * 3) = 48√6.

Answer: 48√6.