What is the number of square units in the area of a triangle whose sides measure 5, 5 and 6 units?
I know that the area of a triangle is given by half the base times the height, but I don't know which side to use as the base and how to find the height. I also know that this is an isosceles triangle, since two sides are equal, and that means that the base angles are equal as well. Maybe I can use the Pythagorean theorem to find the height, if I draw an altitude from the vertex opposite the base to the midpoint of the base. That would divide the triangle into two right triangles, each with a hypotenuse of 5 and a base of 3, since the base of 6 is bisected. By the Pythagorean theorem, the height is then the square root of 5^2 - 3^2, which is the square root of 16, or 4. So the area of the triangle is half of 6 times 4, which is 12. 