CAMBRIA STEEL. 



551 



MENSURATION (Continued) . 



Triangle = base X half perpendicular height. 

 Parallelogram = base X perpendicular height. 

 Trapezoid = half the sum of the parallel sides X perpendicular 



height. 



Trapezium, found by dividing into two triangles. 

 Circle = diameter squared X 0.7854; or, = circumference squared 



X 0.07958. 



Sector of circle = length of arc X half radius. 

 Segment of circle = area of sector of equal radius triangle 



when segment is less, and + triangle when segment is greater 



than the semicircle; also for flat segments very nearly = 

 4v 



- J 



3- 0.388 v4~- 



Side of square of equal area as circle = diameter X 0.8862; also, 



= circumference X 0.2821. 



Diameter of circle of equal area as square = side X 1.1284. 

 Parabola = base X % height. 



Ellipse = long diameter X short diameter X 0.7854. 

 Regular polygon = sum of sides X half perpendicular distance 



from center to sides. 



APPROXIMATE AREA OF IRREGULAR FIGURE. 



Divide figure into n strips by equidistant parallel ordinates, 

 ho, hi, Ii2, etc. 



Then by 



Simpson's Rule, (n must be even) 



Area=-[(h +h)+4(h 1 +h 3 + . . . 



Durand's Rule 

 Area = w[0.4 (h +h 



Trapezoidal Rule 

 Area = w hoh 



(h 2 +h 4 + . . . 



