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" 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. "
Elements of Plane Geometry: For the Use of Schools - Page 87
by Nicholas Tillinghast - 1844 - 96 pages
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Plane Geometry

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...
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Plane Geometry

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...
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Plane Geometry

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...
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Solid Geometry

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....
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Plane and Solid Geometry

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...
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Plane Geometry, with Problems and Application

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...
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Schultze and Sevenoak's Plane and Solid Geometry

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...
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Plane Geometry: With Problems and Applications

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...
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Bulletin, Issues 25-53

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...
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Bulletin

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...
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