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The area of a regular polygon is equal to half the product of its perimeter and apothem.
An Elementary Geometry - Page 43
by William Frothingham Bradbury - 1872 - 110 pages

The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 414 pages
...have their homologous* sides proportional. . • . the polygons are similar. (307) QED 415. COR. 1. The perimeters of regular polygons of the same number of sides are to each other as any two homologous* sides. (322) 416. COR. 2. The areas of regular polygons of the...

Elementary Geometry

William Chauvenet - 1893 - 340 pages
...B'C', or CD : C'D', etc. Therefore the polygons fulfil the two conditions of similarity. 11. COROLLARY. The perimeters of regular polygons of the same number of sides are to each other as the radii of the circumscribed circles, or as the radii of the inscribed circles;...

Elements of Geometry: Plane and Solid

John Macnie - Geometry - 1895 - 390 pages
...similarly, all the sides about the equal A are proportional ; ... P is similar to p'. QED (284) 384 COR. The perimeters of regular polygons of the same number of sides are as their radii, or apothems; and their areas are as the squares of these lines. For the radii and apothems are...

Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...m2 r2 s2 — =- — —='; -'. by substitution — = — ^ = -75 = —^ ' mrs P" a' m'2 r'2 s 2 2. The perimeters of regular polygons of the same number of sides are proportional to their apothems, their radii, or their sides. Proved with cor. 1. EXERCISES. 470. The...

Elements of Geometry

George Washington Hull - Geometry - 1897 - 408 pages
...§ 98 Hence /.A = Z G, ZJ3= Ztf, etc. Therefore ABCDEF and GHKLMN are similar. § 217 324. COR.— The perimeters of regular polygons of the same number of sides are to each other as the radii of the circumscribed circles, or as the radii of the inscribed circles;...

Plane and Solid Geometry

James Howard Gore - Geometry - 1898 - 232 pages
...A'B' + B'C' + C'D' + etc. ~~ A'B ' ' Perimeter of AB - F_ AB . Perimeter of A'B' - F' ~ A'B'' that is, The perimeters of regular polygons of the same number of sides are to each other as any two homologous sides or lines. PROPOSITION III. THEOREM. 292. The area of a regular...

Plane Geometry

William James Milne - Geometry, Modern - 1899 - 258 pages
...with the ratio of any two homologous sides? With the ratio of their radii? Of their apothems? Theorem. The perimeters of regular polygons of the same number of sides are to each other as their radii and also as their apothems. D MG Data : Any two regular polygons of the...

Plane and Solid Geometry

William James Milne - Geometry - 1899 - 398 pages
...the ratio of any two homologous sides? With the ratio of their radii? Of their apothems ? Theorem. The perimeters of regular polygons of the same number of sides are to each other as their radii and also as their apothems. D M a Data : Any two regular polygons of the...