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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. "
An Elementary Treatise on Geometry: Simplified for Beginners Not Versed in ... - Page 138
by Francis Joseph Grund - 1834 - 190 pages
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Elements of Plane Geometry

William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 284 pages
...2£s (§ 193), 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...
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Plane Geometry: With Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1910 - 304 pages
...A'B' +B'C' + C' D' + ••• A'B' r' a' Draw the figure and give the proof in full. 348. THEOREM. The areas of two regular polygons of the same number of sides are in the same ratio as the squares of the corresponding radii or apothems. Outline of Proof : Divide...
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Elements of Plane Geometry

William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 286 pages
...(§ 193), n and are, therefore, equal. .-. ABCDEF ~ GHIKLM. § 363 0. ED 471. COR. 1. The perimeters of two regular polygons of the same number of sides are to each oiher as their radii or as their apothems. BOOK V. PLANE GEOMETRY. PROPOSITION VI. THEOREM. 473. The...
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Plane Geometry: With Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1910 - 300 pages
...} '"' A'B' +B'C' + C'D' + -~ A1B' r'~a'' Draw the figure and give the proof in full. 348. THEOREM. The areas of two regular polygons of the same number of sides are in the same ratio as the squares of the corresponding radii or apothems. Outline of Proof : Divide...
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Plane Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 328 pages
...what is the ratio 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...
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College Entrance Examination Papers in Plane Geometry

Geometry, Plane - 1911 - 192 pages
...triangle is a and the angle at the vertex is 30°; show that the length of the base equals a \/ 2 -\/3. 7. The areas of two regular polygons of the same number of sides are in the same ratio as the squares of the radii of the inscribed or circumscribed circles. JUNE, 1901...
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Plane Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 332 pages
...inches, respectively ; what is the ratio of their areas ? PROPOSITION VIII. THEOREM 538. The perimeters of two regular polygons of the same number of sides are to each otlIer as their radii or as tlIeir apothems. E' Given regular polygons ABCDE and A'B'C'D'S' having...
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Plane and Solid Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry - 1912 - 504 pages
...441, .^ = .4^r> Prove 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...
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Plane Geometry

William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...polygons proportional ? 2. Are the polygons mutually equiangular ? 452. COROLLARY 1. The perimeters of two regular polygons of the same number of sides are to each other as any two homologous sides ; and the areas of two regular polygons of the same number of sides are to...
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Plane Geometry

William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...two arcs having the ratio 1:3 (1:5, 2:3, 3 : 7, 7 : 8). PROPOSITION VI. THEOREM 454. The perimeters of two regular polygons of the same number of sides are to each other as their radii and also as their apothems. Given two regular polygons, each having n sides, and with the...
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