In a quadrilateral ABCD, AB=BC and CD=DA; AC and BD are diagonals such that AC=6 cm and BD=12 cm. What is the area of the quadrilateral?

Explanation

A quadrilateral with two distinct pairs of equal-length sides adjacent to each other (AB=BC and CD=DA) is a kite. A key property of a kite is that its diagonals are perpendicular. Therefore, its area can be calculated using the formula \frac{1}{2} \times d_1 \times d_2. Substituting the diagonal lengths gives \frac{1}{2} \times 6 \times 12 = 36 square cm.

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