Discussion
Which of the following is the area of a rhombus?
Answer: C
The diagonals of a rhombus bisect each other at right angles, cutting it into four congruent right triangles. That gives
\[ A = \frac{1}{2} d_{1} d_{2} \]
Each of the four triangles has area \( \tfrac{1}{2} \cdot \tfrac{d_{1}}{2} \cdot \tfrac{d_{2}}{2} = \tfrac{d_{1}d_{2}}{8} \), and four of them make \( \tfrac{d_{1}d_{2}}{2} \).
The same half-product formula works for any quadrilateral whose diagonals are perpendicular, including the square and the kite.
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