Question

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

• A. a²(2π - 1) sq. units
• B. a²(2 - π) sq. units
• C. (a²/2)(π - 2) sq. units
• D. 2a²(π - 2) sq. units

Answer 1

Answer:

C. (a²/2)(π - 2) sq. units

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