Find the area of the triangle ABC if the CH height is 12, the AC side is 15, BC is 20, AB is 25.

We know from the condition that a triangle ABC is given, and the known length of all three of its sides is AC = 15; BC = 20; AB = 25 and we know the length of the height CH = 12.

In order to find the area of a triangle, we will apply the formula:

S = 1/2 * a * ha;

The area of a triangle is equal to half the product of the side by the height by which it is lowered.

It remains for us to find out on which side the height CH = 12 is lowered.

The height is lowered from the top of C to the AB side.

Substitute the values and get:

S = 1/2 * 25 * 12 = 150 sq. units.