Question

2 formula 2 points fido the dog is on a 11.7 - ft chain that is attached to the middle of the back of a barn, as shown in the picture below. the chain does not allow him to go past either of the adjacent sides of the barn, thereby allowing him to roam all the space inside 1/2 of a circle. how much area does fido have to roam? use 3.14 for pi. round your answer to the nearest tenth, but do not include \sq ft\ or \ft^2\ with your response.

Explanation:

Step1: Recall circle - area formula

The area formula of a full - circle is $A = \pi r^{2}$, where $r$ is the radius of the circle. Here, the radius of the semi - circle $r = 11.7$ ft.

Step2: Calculate the area of the semi - circle

The area of a semi - circle $A_{semicircle}=\frac{1}{2}\pi r^{2}$. Substitute $r = 11.7$ ft and $\pi=3.14$ into the formula: $A_{semicircle}=\frac{1}{2}\times3.14\times(11.7)^{2}$. First, calculate $(11.7)^{2}=136.89$. Then, $\frac{1}{2}\times3.14\times136.89 = 1.57\times136.89=214.9173$.

Step3: Round the result

Round $214.9173$ to the nearest tenth. The digit in the hundredth place is 1, so we keep the digit in the tenth place as it is. The result is $214.9$.

Answer:

$214.9$