Measurement of Area and Volume 25 



in area to the square which has as its side the unit of 

 length employed. 



Example. The adjacent sides of a rectangle are 

 respectively 1'50 in. and 2- 00 in. in length. The area 

 of the rectangle is (T50 x 2' 00) sq. in. = 3 ! 00 square 

 inches. 



Note that we do not say that the area is 1'5 in. x 

 2-0 in. Numbers, but not lengths, may be multiplied 

 together. 



Such an expression as " Multiply together the 

 lengths of two adjacent sides " is, however, com- 

 monly used, but must always be looked upon as simply 

 an abbreviated method of writing " Multiply together 

 the number of units of length in one side by the number 

 of units of length in an adjacent side". 

 (6) Area of parallelogram. 



A parallelogram is a four-sided rectilinear figure 

 which has its opposite sides parallel. 



The area of a parallelogram is found by multiplying 

 the length of one side (such as EF, Fig. 8) by the 

 length of the perpendicular drawn to it from any point 

 on the opposite side. 



Example. The area of the parallelogram EFGH 

 (Fig. 8) is (1-40 x 4'60) sq. cm. = 6'44 sq. cm. 



That this rule is correct may be readily seen if we 

 cut off the triangular portion FKG, and place it at the 

 opposite end of the parallelogram in the position shown 

 by the dotted lines EL, LH, when the parallelogram 

 becomes a rectangle EFKL of which the area is, by 

 our previous rule, equal to the product EF x FK. 

 (c) Area of triangle. 



A triangle is a three-sided rectilinear figure. The 

 area of the triangle MNO (Fig. 8) is evidently half the 

 area of the parallelogram MNOQ, and is therefore 



