What is the shaded area of the figure? (Use\[\pi =\frac{22}{7}\].)
A) \[\text{363 c}{{\text{m}}^{\text{2}}}\]
B) \[\text{259 c}{{\text{m}}^{2}}\]
C) \[\text{3}0\text{5}\,\text{c}{{\text{m}}^{\text{2}}}\]
D) \[\text{216}\,\text{c}{{\text{m}}^{\text{2}}}\]
Correct Answer: B
Solution :
Area of rectangle\[~=\text{ 28 cm}\times \text{23 cm}\] \[=\text{ 644 c}{{\text{m}}^{\text{2}}}\] Radius of semicircle\[~=\text{28 cm}\div \text{2}=\text{14 cm}\] Radius of quadrant\[~=\text{23cm}-\text{16cm}=\text{7cm}\] Area of unshaded region \[=(\frac{1}{2}\times \frac{22}{7}\times 14cm\times 14cm)+\] \[(2\times \frac{1}{4}\times \frac{22}{7}\times 7cm\times 7cm)=385\,c{{m}^{2}}\] Shaded area \[=\text{644 c}{{\text{m}}^{\text{2}}}-\text{385 c}{{\text{m}}^{\text{2}}}\]\[=\text{259 c}{{\text{m}}^{\text{2}}}\]
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