MATHEMATICS 



35 



IRREGULAR AREAS 



Divide the area into trapezoids, triangles, parts 

 of circles, etc., and find the sum of the partial 

 areas. 



If the figure is very irregular, the approximate 

 area may be found as follows: Divide the figure 

 into trapezoids by equidistant parallel lines b, c, d, 

 etc., and measure the lengths of these lines. Then, 

 calling a the first and n the last length, and y the width of strips, 



SECTOR 



If I denotes the length of the arc, and E* the angle in degrees 

 and decimals of a degree, 



Er 



.0175 Er, nearly 



V 



Then, 



57.296 



A = -- = .008727r2 

 360 



CIRCLE 



*If the angle E is stated in degrees, minutes, and seconds, 

 the minutes and seconds must be reduced to decimals of a 

 degree. To do this, divide the number of minutes by 60 and 

 the number of seconds by 3,600 and add the sum of the quo- 

 tients to the number of degrees. Thus, 28 42' 18" = 28 

 8+.7+.005 = 28.705 . 



