| In the figure, ABDCA represents a quadrant of a circle of radius \[\text{7 cm}\]with centre A. Find the area of the shaded portion. |
 s |
A) \[14\,c{{m}^{2}}\]
B) \[24.5\,c{{m}^{2}}\]
C) \[38.5\,c{{m}^{2}}\]
D) \[31.5\,c{{m}^{2}}\]
Correct Answer: D
Solution :
| [d] Area of quadrant \[ABDCA=\frac{1}{4}\pi {{r}^{2}}\] |
| \[=\frac{1}{4}\times \frac{22}{7}\times {{(7)}^{2}}=\frac{77}{2}c{{m}^{2}}=38.5c{{m}^{2}}\] |
| Area of \[\Delta BAE=\frac{1}{2}\times \text{base }\times \text{ height}\] |
| \[=\frac{1}{2}\times AB\times AE=\frac{1}{2}\times 7\times 2=7c{{m}^{2}}\] |
| Hence, area of the shaded portion |
| \[=\text{ Area of the quadrant ABDCA}-\text{Area of }\Delta \text{BAE}\]\[=(38.5-7)\,c{{m}^{2}}=31.5\,c{{m}^{2}}\] |
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