MEASUREMENT OF AREA 



13 



In effect the same result is obtained by multiplying the number 

 of units of length by the number of units of breadth. And it is found 

 that this is true for rectangles of different sizes and shapes. 



Rule. The area of a rectangular figure is found by multiplying the 

 length by the breadth. 



It is important to note that whatever the unit of length used in the 

 measurements, the area will be found in the corresponding unit of 

 area. 



G. AREA OF PARALLELOGRAMS. 



i. Area of parallelograms. Draw two parallel lines a short distance apart 

 upon squared paper. Mark off equal lengths upon one of the lines and 

 construct two parallelograms as in Fig. 10. (Every four-sided figure the 

 opposite sides of which are parallel is a parallelogram. ) Count the number 



FIG. 10. Parallelograms on equal bases and between the same parallels. 



of squares in each parallelogram, and either estimate the fractions of squares 

 near the sides, or, what is easier and generally just as satisfactory, count 

 all parts of squares included in the figure equal to or greater than a half- 

 square as one, and neglect all fractions less than a half square. 



Measure in your book the height of each figure in units, and also the 

 number of units in the base. 



Class results should be collected as before. 



ii. Area of parallelograms (another method). Cut out two cardboard 

 parallelograms A BCD, EFGH (Fig. 11) and draw a line from D perpen- 

 dicular to BC, and from G perpendicular to EF. Cut off the two triangles 

 DLC, GMF, and place them so as to convert each parallelogram into a 

 rectangle. 



Area of parallelograms. If a parallelogram is cut out in card- 

 board, a triangle can be cut off it, such that it can be fitted exactly 

 at the opposite side to form a rectangle (Fig. 11). This is true what- 

 ever the shape of the parallelogram. Evidently the area of each 

 complete figure is the same whether the triangle is in one position or 

 the other. In other words, a parallelogram has the same area as a 

 rectangle on the same base and having the same altitude, or perpen- 

 dicular height. As the area of a rectangle is equal to the base multiplied 





