52 MA THEM A TICS 



EXAMPLE. A segment of a circle having a radius of 7.5 in. 

 is 1.91 in. high and its chord is 10 in. long. If the angle 

 subtended by the chord is 83.46, what is the area of the 

 segment? 



SOLUTION. Substituting the given values in the foregoing 

 formula, 



3.1416X7.52X83.46 10 

 360 2 



= 40.97 27.95 = 13.02 sq. in., nearly. 



If the lengths of the sides of a triangle are known, the area 

 may be found by the formula 

 b 



in which A denotes the area of the triangle and a, b, and c 

 denote the lengths of the three sides. 



EXAMPLE. What is the area of a triangle whose sides are 

 21 ft., 46 ft., and 50 ft. long? 



SOLUTION. In order to apply the formula, let a represent 

 the side that is 21 ft. long; b, the side that is 50 ft. long; and 

 -c, the side that is 46 ft. long. Then, substituting in the 

 formula, 

 50 



_ 



= 25 V441 -8.25 2 = 25 \441 - 68.0625 = 25 \372.9375 



= 25X19.312 = 482.8 sq. ft., nearly. 



EXAMPLE. When x = 8 and y = 6, what is the value of m in 

 the following: _ 



SOLUTION. Substituting, 

 m 



4X8X6 

 16+2.02 = 18.02 



