Find the area of the shaded region in the given figure, where $ABCD$ is a square of side $14\text{ cm}$ and $APD$ and $BPC$ are semicircles.
Step-by-Step Solution
Key Concept: Shaded Area $= \text{Area of square} - 2 \times \text{Area of semicircle of radius } 7\text{ cm} = 14^2 - 2\left(\dfrac{1}{2} \times \dfrac{22}{7} \times 49\right) = 196 - 154 = 42\text{ cm}^2$.
Area of square $= 14 \times 14 = 196\text{ cm}^2$. [1.0 Mark]
Area of 2 semicircles $= 2 \times \dfrac{1}{2} \times \dfrac{22}{7} \times 49 = 154\text{ cm}^2$. [1.0 Mark]
Shaded Area $= 196 - 154 = 42\text{ cm}^2$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Calculating square area $= 196\text{ cm}^2$: 1.0 Mark
Calculating 2 semicircles area $= 154\text{ cm}^2$: 1.0 Mark
Evaluating shaded area $= 42\text{ cm}^2$: 1.0 Mark
Correct Answer: