MEASUREMENT OF AREA 



15 



the method of counting squares, is just one half the product of the 

 base and perpendicular height. 



Rule. To find the area of a triangle multiply the base by the perpen- 

 dicular height and divide by two. 



It does not matter which side is taken as base. 



8. AREA OF A CIRCLE. 



i. Area of a circle. Draw a circle four inches in diameter on gummed 

 paper. (A gummed jam-pot cover may be used.) Divide into small 

 triangles as in Fig. 12. Cut out the 

 triangles neatly and arrange them as in 

 Fig. 13. Moisten the gummed side of 

 the paper and paste into the laboratory 

 notebook. Note the approximate shape 

 of the new figure and express its area 

 in terms of the radius and circumference 

 of the circle. 



The area of a circle. The area of 

 a circle may be found by dividing the 

 circle up into small triangles as shown 

 in Fig. 12, and taking the sum of them. 

 If the triangles are arranged as shown 

 in Fig. 13 a figure closely resembling 

 a parallelogram is formed. The height 

 of this figure is equal to the radius, and the base to half the length of 

 the circumference of the circle. Therefore, since the area of the figure 

 equals that of the original circle, the area of a circle is equal to the 



FIG. 12. Circle divided into triangles. 



FIG. 13. Figure formed by triangles cut from a circular disc. 



radius multiplied by half the circumference. The figure is not a perfect 

 parallelogram, but it is evident that by making the segments much 

 smaller the approximation becomes more perfect. Theoretically 

 there is no limit to the smallness of the triangles, and it may therefore 

 be taken that the above rule is accurate. If for the circumference 



