A parallelogram has sides 12 cm and 9 cm long. The length of one of its diagonals is 15 cm. What is the area (in cm2) of the parallelogram?
108
Since \(9^2+12^2 = 81+144 = 225 = 15^2\), the diagonal of 15 cm splits the parallelogram into two right triangles with legs 9 cm and 12 cm.
Area of the parallelogram: \(2\times\left(\tfrac12\times9\times12\right) = 2\times54 = 108\).
Hence, the area of the parallelogram is 108 cm2.
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