Garden Surveying, Levelling, and Mensuration 225 



comes to the same thing. Thus if a triangle has a base of 9 ft. and 



9 x 4 9x9 



a height of 4^ ft, the area may be found either by - s - = - - - 

 9 99 ^2x2 



= 20 sq. ft; or - x 4 = 2 x ~ = 20 i S <1- ^- A. somewhat more com- 



plicated problem is to find the area of a triangle from the given lengths 

 of the three sides. The rule is: From, half the sum of the three sides 

 subtract each side separately; multiply the half sum, and the three 

 remainders together; the square root of the product will be the area. 

 Example: The sides of a triangle are 26 in., 28 in., and 30 in. respectively. 



84 

 The sum of these is 26 + 28 + 30 = 84. Half the sum is ~ = 42. 



m 



From this subtract each side separately: 42 26 = 16; 42 28 = 14; 

 42 30 = 12. Multiply half the sum and the three remainders together, 

 thus: 42x16x14x12 = 112,896. The square root of 112,896 is the 

 area of the triangle, viz. 336 sq. in. 



The area of an equilateral triangle is readily found by multiplying one 

 side by '433. 



From these examples it will be easy to find the total area of the end 

 of a greenhouse or building by adding the area of the rectangular portion 

 to the area of the triangular portion. 



Other Fig'ures. The area of a rhombus equals half the product of the 

 two diagonals. The area of a trapezoid equals half the sum of two parallel 

 sides by the perpendicular distance between them. 



The area of a trapezium, equals the longest diagonal by half the sum of 

 the two perpendiculars falling upon it from the opposite angles. 



The area of any irregular four-sided figure with straight sides may be 

 found by dividing it into triangles. Find the area of each triangle sepa- 

 rately and add together. 



Volumes. The volume or cubic contents of any body is found by solid 

 or cubic measure, a practical knowledge of which is most useful to com- 

 mercial gardeners. Before proceeding to give examples, the following 

 tables may be noted: 



1 cub. ft. = 1728 cub. in. 



27 cub. ft. = 1 cub. yd. = 46,656 cub. in. 



1 cub. ft. of water = 1000 oz. avoir, (really 997*137 oz.) = 62-5 Ib. 



1 pt. of pure water weighs 1 Ib. 



1 gal. of water = 10 Ib. = 277 cub. in. 



pk. 



1 bush. 



= 8=4=1 qr. 

 = 64 = 32 = 8 = 1 



Thus, to find the cubic contents of any square or rectangular solid body, 



VOL. III. 45 



