Find the area of the shaded region, such that square is formed by using the line

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Find the area of the shaded region, such that square is formed by using the lines x= $\pm$ 1, y= $\pm$ 1.

Options:

A .

\frac{4 - π}{2}

B .

\frac{4 - π}{4}

C . 4 -

π

D . 2(4 -

π

)

Answer: Option A
:
A

From the figure, it is evident the required area = $\frac{A r e a o f S q u a r e - A r e a o f C i r c l e}{4} \times$ 2
Therefore, required area = $\frac{[(2)^{2} - π (1)^{2}]}{4} \times 2 = \frac{4 - π}{2}$
Shortcut: 4-pi-2 method
This is the most straightforward example of the circle inside a square pattern.
Therefore, we know that Area of square: Area of Circle = 4: $π$
Thus,required area = $\frac{4 - π}{2}$

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