What is the area of a regular octagon with a radius of 2? This is actually confusing me because I didn't think octagons had a radius?
A. 11.76
B. 11.31
C. 10.95
D. 10.39

Question

What is the area of a regular octagon with a radius of 2? This is actually confusing me because I didn't think octagons had a radius?
A. 11.76 
B. 11.31 
C. 10.95 
D. 10.39

perl · Answer

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wolf1728 · Answer

Here's a diagram

wolf1728 · Answer

Line CD is called the inradius

anonymous · Answer

Ahhh, so they do..but how would one solve that for this? I have honestly never been asked a question asking for that with an octagon

wolf1728 · Answer

Heck let's just try to solve this by the central angle.
In an octagon, there will be 8 45 degree central angles.

wolf1728 · Answer

We have to figure the area of triangle ABC and then multiply by 8

wolf1728 · Answer

The radius of a regular polygon is the distance from the center to any vertex. So, in my diagram it is AC or AB

wolf1728 · Answer

I hunted around for a polygon calculator and calculated area = 11.309
So, I guess the answer is B

anonymous · Answer

Sorry, I dosed off. I've been at this submission for a while. Thank you so much for the explanation though. I really didn't understand it so again, thanks so much. I appreciate it.