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What is the area included between a circle and an inscribed square of side 'a' units?

Aa²(2π - 1) sq. units

Ba²(2 - π) sq. units

C(a²/2)(π - 2) sq. units

D2a²(π - 2) sq. units

Answer:

C. (a²/2)(π - 2) sq. units

Read Explanation:

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area included between a circle and an inscribed square of side 'a' is area of circle - area of square

area of square = $a^2$

diameter of circle = diagonal length of square

diameter of circle = $\sqrt2 a$

radius of circle = $\frac{\sqrt2 a}{2}$=$\frac{a}{\sqrt2}$

area of circle

= $\pi r^2$

= $\pi \times (\frac{a}{\sqrt2})^2$

= $\pi \times \frac {a^2}{2}$

area included between a circle and an inscribed square of side 'a' is area of circle - area of square

= $\pi \times \frac {a^2}{2}$$-a^2$

= $(\frac{a^2}{2})(\pi-2)$

(a²/2)(π - 2) sq. units


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