14 MATHEMATICS 



where the direction of the curved boundary changes materially, 

 as shown. The area of the polygon AEFMCHIA is calculated 

 by one of the methods previously explained, and from it is 

 subtracted the sum of the areas included between the curved 

 boundary and the broken line, calculated in the manner just 

 shown. 



At such corners as A, the triangles ABC and ABD are 

 computed from the measured bases AC and AD and the 

 altitudes EC and BD. All the quadrilaterals, as QRST, are 

 treated as trapezoids; and such three-sided figures as MPN, 

 as triangles. 



ELLIPSE 



* = * 



-Dd=.7854Dd 

 SECTOR 



A = 



.008727r2E 



360 

 = length of arc 



SEGMENT 



m-E 



.0175rE 



= 57.2956 

 irr r 



RING 



* The perimeter of an ellipse cannot be exactly determined 

 without a very elaborate calculation, and this formula is 

 merely an approximation giving fairly close results. 



nprf 





