 | Eugene Randolph Smith - Geometry, Plane - 1909 - 424 pages
...area of a regular polygon equals one half the product of the perimeter by the apothem. 315. COR. 2. The perimeters of regular polygons of the same number of sides are proportional to their sides, apothems, or radii. 316. COR. 3. The areas of regular polygons of the... | |
 | George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...squares on any two corresponding sides. PROPOSITION IV. THEOREM 375. The perimeters of two regular polygons of the same number of sides are to each other as their radii, and also as their apothems. AMB A' M' B' Given the regular polygons with perimeters p... | |
 | William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 284 pages
...and are, therefore, equal. .-. ABCDEF ~ GHIKLM. §363 QED 471. COK. 1. The perimeters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. BOOK V. PLANE GEOMETRY. PROPOSITION VI. THEOREM. 473. The area of... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 332 pages
...and 441, ^ = -j^. Prove AAOE~&A' O'E' AE A'E' O'A' O'F' (§ 435). 539. Cor. The areas of two regular polygons of the same number of sides are to each other as the squares of their radii or as the squares of their apothems. Ex. 998. Two regular hexagons are inscribed... | |
 | Geometry, Plane - 1911 - 192 pages
...tangency, prove that they are divided proportionally by the smaller circle. 6. The areas of two regular polygons of the same number of sides are to each other as the squares of their radii or their apothems. 6. Prove that if one acute angle of a triangle is double... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 328 pages
...of their perimeters ? of their areas ? PROPOSITION VIII. THEOREM 638. The perimeters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. E A' F' E' Given regular polygons ABCDE and A'B'C'D'E' having the... | |
 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...equal to 3.1416 linear units, nearly. It has been shown (§ 454) that the perimeters of two regular polygons of the same number of sides are to each other as their radii, and hence also as the diameters of their circumscribed circles. Then it may be assumed... | |
 | William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...equal to 3.1416 linear units, nearly. It has been shown (§ 454) that the perimeters of two regular polygons of the same number of sides are to each other as their radii, and hence also as the diameters of their circumscribed circles. Then it may be assumed... | |
 | Clara Avis Hart, Daniel D. Feldman, Virgil Snyder - Geometry, Solid - 1912 - 230 pages
...division form a regular polygon circumscribed about the circle. 538. The perimeters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. 541. I. The perimeter and area of a regular polygon inscribed in... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry - 1912 - 504 pages
...AE (§535 and §428). Then A' . OA _ OF A'E' O'A' O'f (§435). 539. Cor. Tlie areas of two regular polygons of the same number of sides are to each other as tJie squares of their radii or as the squares of their apothems. "Ex.. 998. Two regular hexagons are... | |
| |
The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop. 
