What does that in term of R, r, a mean? I am confusing. tell me the detail of it, please
In each of the figures named in the next few problems the object is to express its area (i) in terms of the radius R, that is, the radius of the circumscribed circle, (ii) in terms of the apothem r, that is, the radius of the inscribed circle, and (iii) in terms of the side a.
251. Equilateral triangle. [See problem 67 above.]
252. Square.
253. Regular pentagon.
254. Regular hexagon.
255. Regular octagon.
The area of a regular n-gon is A = nra/2. To find A in terms of R, r, or a, use the relationships
cos 180°/n = r/R, and
tan 180°/n = a/(2r).
Then
(i) in terms of R, the area A = nR^2 cos 180°/n sin 180°/n,
(ii) in terms of r, the area A = nr^2 tan 180°/n, and
(iii) in terms of a, the area A = na^2/(4tan 180°/n).
2007-06-27
16:46:49
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1 answers
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asked by
liangjizong22
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