Question

a square has a side that measures 11 units. what is the area of a circle with a circumference that equals the perimeter of the square? use 3.14 for π, and round your answer to the nearest hundredth. 1519.76 units² 379.94 units² 616.56 units² 154.14 units²

Explanation:

Step1: Calculate the perimeter of the square

The side of the square $s = 11$ units. The perimeter of a square $P=4s$. So, $P = 4\times11=44$ units.

Step2: Find the radius of the circle

The circumference of the circle $C$ is equal to the perimeter of the square, so $C = 44$ units. The formula for the circumference of a circle is $C = 2\pi r$. Given $\pi=3.14$, we can solve for $r$: $44=2\times3.14\times r$. Then $r=\frac{44}{2\times3.14}=\frac{44}{6.28}\approx7.0064$ units.

Step3: Calculate the area of the circle

The formula for the area of a circle is $A=\pi r^{2}$. Substitute $r\approx7.0064$ and $\pi = 3.14$ into the formula: $A=3.14\times(7.0064)^{2}=3.14\times49.0896\approx154.14$ square - units.

Answer:

154.14 units²