| Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...similar. Suggestion. The student can prove this by showing a close connection with Art. 226. Corollary 1. **The perimeters of two regular polygons of the same number of sides are** proportional to their sides, to their apothems, to their radii. Corollary 2. The areas of two regular... | |
| Edith Long, William Charles Brenke - Geometry, Plane - 1916 - 292 pages
...Two regular polygons of the same number of sides are similar. Corollary 1. The perimeters of regular **polygons of the same number of sides are to each other as** their apothems, as their radii, to their sides. Corollary %. The areas of regular polygons are to each... | |
| Fletcher Durell, Elmer Ellsworth Arnold - Geometry, Plane - 1917 - 330 pages
...§317. 3. § 372, Ax. 1. 4. §188. 5. §311. 6. §§302,316. 7. Ax. 1. OED378. COR. The areas of regular **polygons of the same number of sides are to each other as the** squares of the radii of the inscribed, or circumscribed, circles. Ex. 1. If the sides of two regular... | |
| Claude Irwin Palmer - Geometry, Solid - 1918 - 192 pages
...regular polygon is equal to half the product of the perimeter by the apothem. § 479. Theorem. The areas **of two regular polygons of the same number of sides are to each other as the** squares of their radii, and also as the squares of their apothems. . MEASUREMENT OF THE CIRCLE § 485.... | |
| Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry - 1918 - 460 pages
...sum of the areas of the triangles is the area of the polygon, .-. A - %ap. 479. Theorem. The areas **of two regular polygons of the same number of sides are to each other as the** squares of their radii, and also as the squares of their apothems. EXERCISES 1. Prove that the area... | |
| Herbert Ellsworth Slaught - 1918 - 344 pages
...the same number of sides is equal to the ratio of similitude of the two polygons. . 476. COROLLARY 2. **The perimeters of two regular polygons of the same number of sides are** in the same ratio as their radii or as their apothems. AREA OF A REGULAR POLYGON 478. THEOREM V. The... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...But P:P' = AB:A'B' = AD:A'D'. (Why?) ...P:P' = OD:O'D' = AO:A'0'. QED 417. COR. The areas of regular **polygons of the same number of sides are to each other as the** squares of their radii or apothems. Ex. 1315. The lines joining the mid.points of the radii of a regular... | |
| Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1918 - 360 pages
...the same number of sides is equal to the ratio of similitude of the two polygons. 476. COROLLARY 2. **The perimeters of two regular polygons of the same number of sides are** in the same ratio as their radii or as their apothems. AREA OF A' REGULAR POLYGON 478. THEOREM V. The... | |
| United States. Office of Education - 1921 - 1286 pages
...and its external segment. 21. Parallelograms or triangles of equal bases and altitudes are equal. 22. **The perimeters of two regular polygons of the same number of sides are to each other as** their radii and also as their apothème. SOL[D GEOMETRY. In the following list the precise wording... | |
| Education - 1921 - 1190 pages
...and its external segment. 21. Parallelograms or triangles of equal bases and altitudes are equal. 22. **The perimeters of two regular polygons of the same number of sides are to each other as** their radii and also as their apothems. SOLID GEOMETRY. In the following list the precise wording and... | |
| |