 | Rutgers University. College of Agriculture - 1887 - 222 pages
...reciprocally proportional. 4. Similar polygons are to each other as the squares of their homologous sides. 5. The area of a regular polygon is equal to one-half the product of its apothegm by its perimeter. 6. Similar segments are to each other as the squares of their radii. —... | |
 | George Albert Wentworth - Geometry - 1888 - 264 pages
...circle whose diameter is 2 R and circumference O, we have = JT, or C PROPOSITION VIII. THEOREM. 421. The area of a regular polygon is equal to onehalf the product of its apothem by its perimeter. AMB Let P represent the perimeter, R the apothem, and 8 the area of the regular polygon ABC, etc. To... | |
 | George Albert Wentworth - Geometry - 1888 - 272 pages
...diameter is 2 R and circumference C, we have c. s - tr, or 'J = <u Jv PROPOSITION VIII. THEOREM. 421. The area of a regular polygon is equal to onehalf the product of its apothem by Us perimeter. MB Let P represent the perimeter, R the apothem, and 8 the area of the regular polygon... | |
 | George Albert Wentworth - Geometry, Analytic - 1889 - 264 pages
...for any circle whose diameter is 2 R and circumference C, we have C PROPOSITION VIII. THEOREM. 421. The area of a regular polygon is equal to onehalf the product of its apothem by its perimeter. E A if B Let P represent the perimeter, R the apothem, and S the area of the regular polygon ABC, etc,... | |
 | George Irving Hopkins - 1891 - 210 pages
...number of sides are in the same ratio as the squares of the radii of their circumscribed circles. 498. The area of a regular polygon is equal to one-half the product of its perimeter and apothegm. Sug. Draw radii, then consult 485. 499. Any curved or polygonal line which... | |
 | William Shaffer Hall - Measurement - 1893 - 88 pages
...12) + 0 (0 - 18)] = 118.5 square feet. Ans. § 32. To find the area of a regular polygon. [23] RULE: The area of a regular polygon is equal to one-half the product of the perimeter and apothem. For Proof: See Ww. Geom., 379. When the apothem is not given, it may be... | |
 | George Clinton Shutts - Geometry - 1894 - 412 pages
...АО2 МО2 To prove that — = = - — . S HS* AT S2 PLANE GEOMETRY. PROPOSITION VIII. 368. Theorem. The area of a regular polygon is equal to one-half the product 0} its perimeter and apothem. A — ...g Let AD be a regular polygon, 0 N its apothem, and ABC, etc.,... | |
 | Michigan. Department of Public Instruction - Education - 1896 - 710 pages
...diameter, this perpendicular is a mean proportional between the segments of the diameter. ' 9. Demonstrate: The area of a regular polygon is equal to one-half the product of its apothem into its perimeter. 10. Demonstrate: If the opposite sides of a quadrilateral are equal, the figure... | |
 | George D. Pettee - Geometry, Modern - 1896 - 272 pages
...grams to the square centimeter, find the weight of the sheet in kilos. , PROPOSITION XVI 272. Theorem. The area of a regular polygon is equal to one-half the product of its perimeter and apothem. Appl. Cons. Dem. Q The area of ABCDE = Draw radii. Draw OF (apothem) A AOE EOD... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 376 pages
...6 feet; how far does the wheel roll on the track in one revolution ? PROPOSITION XI. THEOREM 47 1. The area of a regular polygon is equal to one-half the product of its apothem and perimeter. AB GIVEN — a regular potygon ABCDE, R its apothem, and P its perimeter. To PROVE area... | |
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The area of a regular polygon is equal to onehalf the product of its apothem and perimeter. 
