trigonometry problems?

Question

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).

Answer 1

In terms of R means that the answer will have an R in it (or r or a).

Example, square: If the side is a, the area is a^2
If the inscribed circle has radius r, in effect a = 2r, so tha area is 4r^2
Given radius R, using the pythagorean theorem
R^2 = 2(a/2)^2 = 1/2 (a^2), so the area = 2R^2

Follow the same logic for all your problems.

Or use the formula. For square n=4
So in terms of r A = 4r^2 (tan45) = 4r^2 (tan45=1)
in terms of R, A= 4R^2 cos45 sin45 = 2R^2

So for triangle n=3, etc.