ABCD is a square with sides of 1 unit. AC and BD are arcs of circles with their centers at B and A. respectively. The area of the shaded sector AED is

Correct option is A

Given:

ABCD is a square with sides of 1 unit. AC and BD are arcs of circles with their centers at B and A, respectively.

Concept:

To find shaded area we subtract the empty area from area of unit cube.

Solution:

$$\begin{aligned}&\textbf{} \quad \text{Since } \triangle ABE \text{ is an equilateral triangle.} \\[6pt]&\text{So, area of sector AEB } = \frac{\pi}{6} \\[6pt]&\text{Area of DBCD } = \text{Area of square} - \frac{1}{4} \times \text{Area of circle} = 1 - \frac{\pi}{4} \\[6pt]&\text{Shaded area} = \text{Area of square} - \text{Area of DBCD} - \text{Area of sector AEB} \\[6pt]&= 1 - (1 - \frac{\pi}{4}) - \frac{\pi}{6} = \frac{\pi}{4} - \frac{\pi}{6} = \frac{\pi}{12} \\[6pt]&\boxed{\text{Hence, shaded area} = \frac{\pi}{12}}\end{aligned}$$​