Explanation

This figure looks a bit like a trapezoid, but it's not a trapezoid: it has five sides, not four, and it doesn't have two parallel bases. It also resembles a rotated square that has been sliced; this resemblance will be more useful. Since there are three right angles and two equal sides, a square can be formed that contains this shape: the two short sides will have to intersect if we extend them, and they will have to form a right angle, since they are perpendicular to each other, meaning the extended shape is a square.

That means that the missing portion is a right triangle with sides 8 and 8. Those two sides are a valid base-height pair, so the area of that triangle is



Meanwhile, the area of the square is . The area of this shape in question is that of the square minus the area of the triangle, so it is



The correct answer is (C).