question_answer

The given figure is made up of a rectangle and 2 identical circles. Given that the length of the rectangle is 28 cm.

A)  \[\text{119 c}{{\text{m}}^{\text{2}}}\]                                 

B)  \[\text{1}0\text{5 c}{{\text{m}}^{\text{2}}}\]

C)  \[\text{152}\,\text{c}{{\text{m}}^{\text{2}}}\]                 

D)  \[\text{123 c}{{\text{m}}^{\text{2}}}\]

Correct Answer: A

Solution :

 Combine the shaded parts in the given figure as in the following figure. Radius of circle\[~=\text{28 cm}\div \text{4}=\text{7 cm}\] Area of quadrant\[=\frac{1}{4}\times \frac{22}{7}\times 7\times 7\]\[=\text{ 38}.\text{5 c}{{\text{m}}^{\text{2}}}\] Area of shaded region \[\text{=(14}\times \text{14)}-\text{38}.\text{5}~-\text{ 38}.\text{5}\] \[=\text{196 c}{{\text{m}}^{\text{2}}}-\text{77 c}{{\text{m}}^{\text{2}}}=\text{119 c}{{\text{m}}^{\text{2}}}\]