WAEC Mathematics 2012 Paper

Concept:The diagonals of a rhombus bisect each other at right angles, so a right triangle is formed by half of each diagonal and one side.Explanation:Let one diagonal be $d_1 = 12\text{ cm}$.Half of this diagonal is $6\text{ cm}$.The side of the rhombus is the hypotenuse of the right triangle, so side $= 10\text{ cm}$.Let half of the other diagonal be $x\text{ cm}$.Using Pythagoras' theorem:$$x^2 + 6^2 = 10^2$$$$x^2 + 36 = 100$$$$x^2 = 64$$$$x = 8\text{ cm}$$So the full other diagonal is:$$d_2 = 2 \times 8 = 16\text{ cm}$$Area of a rhombus $= \frac{1}{2} \times d_1 \times d_2$$$= \frac{1}{2} \times 12 \times 16 = 96\text{ cm}^2$$Answer:D. $96\text{ cm}^2$