In rhombus ABCD, AB = 7.5 cm, and AC = 12 cm. Find the area of the rhombus.

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Solution

In $△ A B O, ∠ A O B = 90 °, A O = \frac{1}{2} A C = 6 c m,$
AB = 7.5 cm

$∴ O B^{2} = A B^{2} - O A^{2} = {(7.5)}^{2} - 6^{2} = 56.25 - 36 = 20.25$

$∴ O B = \sqrt{20.25} = 4.5 c m$

$∴ B D = 2 \times O B = 9 c m$

Area of rhombus $= \frac{1}{2} d_{1} \times d_{2} = \frac{1}{2} \times 9 \times 12 c m^{2} = 54 c m^{2}$

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