Question

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

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

Answer 1

Answer: (B)

Area of circle is larger

Answer 2

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

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

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

$\therefore$ $\frac { \text { Area of circle } } { \text { Area of square } } = \frac { \pi r ^ { 2 } } { \pi ^ { 2 } r ^ { 2 } / 4 } = \frac { 4 } { \pi } > 1$.

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