XXX 



MENSURATION. 



c. Area of regular polygon. 



A = area, 

 r, R =. radii of inscribed and circumscribed circles, 

 s = length of any side, 

 n = number of sides, 

 /3 = angle subtended hy s = 360°///. 



A = nr^tanl^ (3 = ^nR^sm (3 = ^n s^' cot ^ /3. 



Table of Values. 



d. Area of circle, circular annulus, etc. 



r =■ radius of circle, 



d = diameter, 



a = angle of any sector, 

 ri, n = smaller and greater radii of an annulus. 



Area of circle = tt r"^ = I -n- d% 

 7r = 3.14 159 265, log TT — 0.49714987. 



Area of sector = a r", for a in arc, 



= TT r- (a/360), for a in degrees. 



Area of annulus = tt (r.J^ — ?'^). 



e. Area of ellipse. 

 a, b ■= semi axes respectively 

 e = eccentricity = (a^ — b'^yja 

 = {{a^b){a-b)yja. 



