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" 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. "
An Elementary Treatise on Geometry: Simplified for Beginners Not Versed in ... - Page 117
by Francis Joseph Grund - 1834 - 190 pages
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Plane Geometry

Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...same number of sides are proportional to their sides, to their apothems, to their radii. Corollary 2. The areas of two regular polygons of the same number of sides are proportional to the squares of their sides, to the squares of their apothems, to the squares of their...
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Plane Geometry, with Problems and Application

Herbert Ellsworth Slaught - 1918 - 344 pages
...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 area of a regular polygon...
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Plane Geometry: With Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1918 - 360 pages
...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 area of a regular...
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Solid Geometry

Claude Irwin Palmer - Geometry, Solid - 1918 - 192 pages
...of a 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...
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Plane and Solid Geometry

Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry - 1918 - 460 pages
...polygon, and the 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....
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General Mathematics, Book 2

Raleigh Schorling, William David Reeve - Mathematics - 1922 - 476 pages
...quotients are equal. . 4. This is obvious from 3. 5. By definition of similar polygons. 534. Corollary. The areas of two regular polygons of the same number of sides are to each other as the squares of their sides. 535. Theorem. The perimeter of two regular polygons of...
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Essentials of Plane Geometry

David Eugene Smith - Geometry, Plane - 1923 - 314 pages
...corresponding sides of P and P' are proportional. . ' . P and P' are similar. § 205 279. Corollary. The areas of two regular polygons of the same number of sides are to each other as the squares on any two corresponding sides. FUNDAMENTAL THEOREMS BOOK V Proposition...
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Plane Geometry: (Revised)

Claude Irwin Palmer, Daniel Pomeroy Taylor, Eva Crane Farnum - Geometry, Modern - 1924 - 360 pages
...the polygon, the sum of the areas of the triangles is the area of the polygon. ... A = 437. 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. § 387 (2)...
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Mathematics: Course of Study for Senior and Junior High Schools

Baltimore (Md.). Department of Education - Mathematics - 1924 - 182 pages
...polygons of the same number of sides are similar. 7. Two circles arc to each other as their radii. a. The areas of two regular polygons of the same number of sides are to each other as the squares of their sides, or as the squares of their radii. b. The areas of two...
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