Question

In figure, a circle is inscribed in a square. Calculate the area of the shaded portion, to the nearest hundredth.

• A. $10.52m^2$
• B. $21.03m^2$
• C. $22.6m^2$
• D. $42.06m^2$
• E. $84.13m^2$

Answer 1

The correct option is A $10.52m^2$

In figure, the perpendicular of square is $19.8$

We know $(19.8{)}^2=(a{)}^2+(a{)}^2=2(a{)}^2$

Then side $a=$ $19.8/\sqrt{2}$

And radius $r=$ $\frac{a}{2}$

Then area of shaded portion $=$ $(19.8/\sqrt{2}{)}^2-\pi (\frac{a}{2}{)}^2$

$=10.51$