Question

If a circle and a square have the same perimeter, then

• A. Their areas are equal
• B. Area of circle is larger
• C. Area of square is larger
• D. None of these

Answer 1

The correct option is B

Area of circle is larger

We are given that, the perimetre of the circle is equal to the perimetre of square.

$\therefore$ Let ‘r’ be the radius of circle and ‘a’ be the side of square.

$\therefore 2\pi r=4a\Rightarrow a=\frac{\pi r}{2}$

$\therefore$ Area of square $\Rightarrow a^2=\frac{{\pi }^2{r}^2}{4}andareaofcircle=\pi r^2$

$\therefore \frac{Areaofcircle}{Areaofsquare}=\frac{\pi r^2}{{\pi }^2{r}^2/4}=\frac{4}{\pi }>1.$

Thus, area of circle is larger than area of square.