What is area (in sq units) of a triangle with sides 10, 10 and 12?

The triangle with sides 10, 10, and 12 is an isosceles triangle. To find the area of an isosceles triangle, we can use the formula:

Area = 1/2 * base * height

However, we don't have the height. We can find it using the Pythagorean theorem because in an isosceles triangle, if you draw a line from the apex to the base, it will be perpendicular to the base and bisect it, forming two right triangles.

The base of each right triangle is half of the base of the isosceles triangle (which is 12/2 = 6 units) and the hypotenuse is one of the equal sides of the isosceles triangle (which is 10 units).

So, we can find the height (h) using the Pythagorean theorem:

h = sqrt(hypotenuse^2 - base^2) = sqrt(10^2 - 6^2) = sqrt(100 - 36) = sqrt(64) = 8 units

Now, we can find the area of the isosceles triangle:

Area = 1/2 * base * height = 1/2 * 12 * 8 = 48 square units.