Question

This is for a geometry test i'm studying for, help!!

Answer 1

Check the picture below.

so, we know this is a square, so all sides are the same length, but that simply also means that the altitude or height of the inscribed triangle is 36, as well as its base.

so, if we take the area of the square, that will include the area of the triangle, of course that's simply 36*36.

however, if we also take the area of the inscribed triangle and then subtract that much from the area of the square, we're in effect making a triangular hole in the square, and what's leftover, is the shaded area.

`\bf \stackrel{\textit{square's area}}{(36\cdot 36)}~~-~~\stackrel{\textit{triangle's area}}{\cfrac{1}{2}(36)(36)}\implies 1296~~-~~648\implies 648`