MATHEMATICS 



11 



RECTANGLE AND PARALLELOGRAM 



A=ab 



TRAPEZOID 



Case I. Given the two bases bi 

 and 62 and the altitude h, 



Case II. Given the bases and the angles adjacent to one 

 of them, . 



2(cot A+cotB)' 

 (bi 62) (bi + 62) sin A sin B 



2 sin (A + B) 

 Case III. Given the four sides, 



A= 



in which 5= %(a-\-c-\-d) 



TRAPEZIUM 

 Divide into two triangles and a trapezoid. 



or. A = l[bh'+ch+ a(h'+K)] 

 Or, divide into two triangles by drawing a 

 diagonal. Consider the diagonal as the base 

 of both triangles, call its length I; call the alti- 



tudes of the triangles hi and hr, then 

 A = 



OTHER POLYGONS 



The area of any polygon can be determined by dividing the 

 polygon into triangles and measuring in each triangle whatever 

 parts are necessary for the determination of its area. The 

 parts to be measured depend on special conditions. If in 

 surveying a closed field the chain alone is used, the three 

 sides of each triangle will have to be measured and the formula 

 for Case II, page 10, used. If a transit or a compass is used, 

 angles can be measured and the formulas of Cases III or IV, 



