Question

select the correct answer.
a water wheel is designed in the shape of a regular octagon. what is the perimeter of the water wheel?
a. ( 8sqrt{10}\text{ft} )
b. ( 8\text{ft} )
c. ( 80\text{ft} )
d. ( sqrt{10}\text{ft} )

Explanation:

Step1: Calculate the side - length using the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). For the points \((4,0)\) and \((3,3)\), we have \(x_1 = 4,y_1=0,x_2 = 3,y_2 = 3\).

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Step2: Calculate the perimeter of the regular octagon

The perimeter \(P\) of a regular octagon with side - length \(s\) is \(P = 8s\). Since \(s=\sqrt{10}\), then \(P=8\sqrt{10}\).

Answer:

A. \(8\sqrt{10}\text{ ft}\)