Question

Marissa has a wool rug that has the shape of a regular octagon in her living room. The diameter of the incircle of the rug measures 7 feet approximately. Which of the following is the approximate measure of one of the sides of wool rug?
A.2.9 feet
B. 3.5 fest
C. 3.7 feet
D. 4.1 feet

Answer 1

We know that the diameter of the inner circle (d) and the side of a regular octagon (s) are tied by the formula:

d = (1 +√2) × s

The inverse formula is:

s = d / (1 +√2)

Plugging in numbers:
s = 7 (1 + √2)
   = 2.9 ft

Therefore the correct answer is A) 2.9 feet

Answer 2

Answer:

2.9 feet

Step-by-step explanation:

I did it a different way. One including trigonometry. The question only tells the apothem, "diameter of the incircle." Apothem is the line segment from the center to the midpoint of segments in regular polygons. Incircle is a circle that connects all the midpoints in a regular polygon. You are trying to find the side. The angle of view is from the central angle, which is 45 degrees in an octagon. We have to split 45 in half, because when you try to find distance in a line segment, you do it through trig and trig requires a right triangle. Since you are finding the side, you need tangent. The angle of view (I don't know if that's the actual name), it touches the apothem, which would be adjacent. The line that the angle isn't touching is the  opposite. And tanganent uses both of those. The formula I used is tan(22.5)/1 = o/7. These are fractions. Then you cross multiply the fractions, so tan(22.5) goes with 7 and o goes with 1. When you cross multiply, you pretty much multiply the opposite fraction's side. The formula then would be o = tan(22.5) x 7. And that equals 2.9.

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