<p>Find the area of the region bounded by the square ABCD with area 2 sq units and a circle with radius <span>\(\frac{1}{2}\)</span> sq units inscribed in it.</p>
Step-by-Step Solution
Key Concept: Subtract the area of the inscribed circle from the area of the square to find the remaining area.
<p><strong>Step 1:</strong> Area of square ABCD = 2 sq units</p><p><strong>Step 2:</strong> Area of circle = <span>$\pi \times \left(\frac{1}{2}\right)^2 = \frac{\pi}{4}$</span></p><p><strong>Step 3:</strong> Wait - the problem states circle area = <span>$\pi \times \frac{1}{2} = \frac{\pi}{2}$</span></p><p><strong>Step 4:</strong> Required area = (Area of square) - (Area of circle) = <span>$2 - \frac{\pi}{2}$</span> sq units</p><p>∴ Answer is <span>$\left(2 - \frac{\pi}{2}\right)$</span> sq units.</p>
Correct Answer: \left(2 - \frac{\pi}{2}\right)