28 Domestic Science 



the figures have been straight lines. We will now 

 describe a method of finding the area of any plane 

 figure, whatever the nature of its sides. 



EXPERIMENT 7. Fig. 9 shows a rectangle 6 -00 in. 

 long and 4' 00 in. broad, divided up by thick lines 

 into squares each side of which is half an inch long, 

 these being further divided by fainter lines into small 

 squares of which the length of side is one-tenth (O'l) 

 inch. Thus the whole rectangle is divided up into 

 small squares the area of each of which is 



(TO x TO) sq. in. = T J F sq. in. = 0*01 sq. in. 



(To verify this, count the number of little squares 

 in the square ABCD, which has sides 1 in. long, and 

 hence is 1 sq. in. in area.) 



In the middle of the squared paper an irregular 

 figure MNOPQR has been drawn. To find the area 

 of this figure we count the number of little squares 

 enclosed within the boundary of the figure. Since the 

 boundary cuts many of the little squares into two or 

 more parts, we must find in some way the areas of the 

 little pieces of the figure thus cut off. This may be 

 done by estimating by eye what fraction of a whole 

 square each little piece is, and finding the sum of all 

 the fractions. Adding this sum to the total number 

 of complete small squares within the figure gives as 

 a result the area of the figure, expressed in hundredths 

 of a square inch. Dividing this result by 100, the area 

 in square inches is obtained. 



It is easier in general, however, to count each frac- 

 tion of a square larger than half a square as a whole 

 square, and to ignore parts of less area than half a square. 

 Should a square be cut exactly in half it may be counted 

 as half a square. In doing this, we assume that the error 



