MEASUREMENT OF SURFACES. 



nient of the dimensions of the surface. If the surface is 

 rectangular (fig. 1), its area in square units is the pro- 

 duct of the linear units in its length and breadth. Thus, 

 if the figure has a length of 5 centimetres, and a breadth 

 of 3 cm , it can be actually cut up into 15 squares, each 



FIG, 1 (real size), 



having an area of one square centimetre, and its super- 

 ficial area will evidently be 3 x5 = 15 square centimetres. 

 A parallelogram which is not rectangular, abed 

 (fig. 2), can be converted into a rectangle by cutting off 

 a triangle a b e at one end, and putting it on at the other. 

 The parallelogram abed has, therefore, an equal area 

 with the rectangle e b cf, and its magnitude is found by 

 b c d 



/a 



/L 



e ~<r~ f 



FIG. 2 (real size). 



FIG. 3. 



multiplying one of two opposite parallel sides, a d or b c, 

 into their perpendicular distance e b ; a b c d (fig. 2) has 

 an area of 2 x 3 = 6 square centimetres. 



A triangle may be considered as half a parallelogram ; 

 a b c (fig. 3) is half of a b c d. The area of the triangle 



B 2 



