The area of the rectangular pen is 10,000 m² and the area of the circular pen is 12,738.95 m².
For the rectangular pen, we want the sides to be congruent. To minimize perimeter and maximize area, the figure needs to be equilateral.
400/4 = 100 m for each side
This means that the area is 100(100) = 10,000 m².
If the pen is circular, this means the circumference is 400 m. Circumference is given by the formula C=πd:
400 = 3.14d
Divide both sides by 3.14:
400/3.14 = 3.14d/3.14
127.389 = d
The radius is half of the diameter:
r = 127.389/2 = 63.6945
The area of the circle is given by A=πr²:
A=3.14(63.6945)² = 12738.9465 ≈ 12738.95 m²
