| The area of the shaded region in figure, if ABCD is a square of side 14 cm and APD and BPC are semi circles is |
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A) \[196\text{ }c{{m}^{2}}\]
B) \[84c{{m}^{2}}\]
C) \[21c{{m}^{2}}\]
D) \[42c{{m}^{2}}\]
Correct Answer: D
Solution :
Given, side of square =14 cm Also, APD and BPC are semi-circles, therefore Their radius, \[r=\frac{14}{2}=7\,cm\]. Now, area of semi-circle APD = Area of semi-circle \[=\frac{\pi {{r}^{2}}}{2}\] \[=\frac{22}{7\times 2}\times {{\left( 7 \right)}^{2}}=77c{{m}^{2}}\] and area of square \[ABCD={{\left( Side \right)}^{2}}={{\left( 14 \right)}^{2}}\] \[=196\text{ }c{{m}^{2}}\] Hence, area of shaded region = Area of square - (Area of semi-circle APZ) + Area of semi-circle BPC) \[=196-\left( 77+77 \right)=42\text{ }c{{m}^{2}}\]
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