Question 49

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waecmaths question: 

A side and diagonal of a rhombus are 10cm and 12cm respectively. Find its area

Option A: 

20cm2

Option B: 

24cm2

Option C: 

48cm2

Option D: 

96cm2

waecmaths solution: 

\[\begin{align}  & \text{Consider }\Delta ADB \\ & \text{Using cosine rule} \\ & \cos A=\frac{{{b}^{2}}+{{d}^{2}}-{{a}^{2}}}{2bd}=\frac{{{10}^{2}}+{{10}^{2}}-{{12}^{2}}}{2\times 10\times 10} \\ & \cos A=\frac{56}{200}=0.28 \\ & A={{\cos }^{-1}}(0.28)={{73.74}^{\circ }} \\ & \text{Area of }\Delta DAB=\tfrac{1}{2}bd\sin {{73.74}^{\circ }} \\ & =\tfrac{1}{2}\times 10\times 10\sin {{73.74}^{\circ }} \\ & =48c{{m}^{2}} \\ & \text{Area of the Rhombus }=2\times \text{Area of }\Delta DAB \\ & \text{Area of the Rhombus}=2\times 48c{{m}^{2}}=96c{{m}^{2}} \\\end{align}\]

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