Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

If a string with length of 20 cm was to create a rectangle and circle, would area of these objects be the same?

share|improve this question

3 Answers 3

No. The circle will always have larger area than the rectangle. See http://en.wikipedia.org/wiki/Isoperimetric_inequality.

share|improve this answer

No. You can even create two rectangles with different areas but the same perimeter, e.g. sides 4 and 6 (area 24) and sides 1 and 9 (area 9).

share|improve this answer

No, the circle is the shape with the largest area for its perimeter. From $C=2\pi r$ we find $r=\frac{10}{\pi}$ and $A=\pi r^2=\frac {100}{\pi} \approx 31.83 \text{cm}^2$. This is larger than both rectangles mentioned by Chris Card. A square would have area $25\text{cm}^2$

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.