SUE 



13 



2. The area of a trapezium rr base X | sum of the perpendiculars. 

 And the area of a trapezoid j= | sum of the parallel sides X perpendicular 

 distance between them. 



3. To find the area of any irregular polygon, divide it into trapeziums, 

 or trapczoids, or triangles, and find their areas separately ; and their sum 

 is the area of the polygon. 



4. To find the area of a long irregular figure E q D p bounded on one 

 side by a curve. 



Divide ED into any number of equal parts, and measure the perpen- 

 diculars, no,pg, rs, tv c. then the area is found nearly by adding to- 

 gether all the perpendiculars, dividing the sum by the number of per- 

 pendiculars increased by unity, and multiplying by the chord of the 

 curve. 



5. Tofinrl, by the forego- 

 ing rules, i he, content of 

 theirregular field ABCDE, 

 which will include most of 

 the cases likely to occur in 

 practice. 



Find the area of the tra- 

 pezium A B D E by Art. 3, 

 the A B D C by Art. 1 ; and 

 the curvilinear areas E q D, -A. B 



E b A by Art. 4 ; add the three first areas together and subtract the last, 

 for the content of the field. , 



Land is measured by a chain 22 yards long, and divided into 100 equal 

 parts or links, each link being 7.92 inches : 10 square chains, or 100,000 

 square links, is one acre, viz. : 



625 square links is 1 perch. 



25,000 square links or 40 perches, 1 rood. 



100,000 square links or 4 roods, 1 acre. 



The perch (which in statute measure is 16| feet) varies by custom ia 

 different parts of England ; and with it, consequently, varies the acre ia 

 proportion. 



In Devonshire and part of Somersetshire, 15; in Cornwall, 18 ; in Lan- 

 cashire atid Yorkshire, 21 j and in Cheshire and Staffordshire, 24, feet are 

 accounted a perch. 



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