SAT Question cf53cb56: Area and Volume answer and explanation with Desmos solution

Choice C is correct. The two diagonals of square $ABCD$ divide the square into $4$ congruent right triangles, where each triangle has a vertex at the origin of the graph shown. The formula for the area of a triangle is $A=\frac{1}{2}\times bh$, where $b$ is the base length of the triangle and $h$ is the height of the triangle. Each of the $4$ congruent right triangles has a height of $5$ units and a base length of $5$ units. Therefore, the area of each triangle is $A=\frac{1}{2}\times 5\times 5$, or $12.5$ square units. Since the $4$ right triangles are congruent, the area of each is $\frac{1}{4}$ of the area of square $ABCD$. It follows that the area of the square $ABCD$ is equal to $4\times 12.5$, or $50$ square units.