A kite has diagonals of length 10 and 16. What is its area?

The area of a kite, or any quadrilateral with perpendicular diagonals, is half the product of the diagonals: $A=\frac{1}{2}d_1d_2=\frac{1}{2}(10)(16)=80$, choice C. This works because the diagonals split the kite into four right triangles whose areas add up to half of the rectangle formed by the diagonals. Choice D ($160$) is the full product with the factor of $\frac{1}{2}$ left out. Choice A ($26$) adds the diagonals. Choice B ($52$) doubles the sum. Area should be measured in square units, so it comes from multiplying, not adding.