 | John Wesley Young, Albert John Schwartz - Geometry, Modern - 1915 - 248 pages
...site sides of this diagonal are equal. A EKD = A DKH, smdAKGB=A KBF. 7 IF PLANE GEOMETRY 361. THEOREM. The area of a regular polygon is equal to half the product of its apothem by its perimeter. Given the regular polygon ABCDEF, with the apothem r and perimeter />. To... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1915 - 282 pages
...these polygons are similar K AB2 B* r3 (287). (411). (376). (Ax. 1). QED PROPOSITION VII. THEOREM 421. The area of a regular polygon is equal to half the product of the perimeter by the apothem. D Given: (?). To Prove: (?). Proof : Draw radii to all the vertices,... | |
 | Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry, Plane - 1915 - 320 pages
...AO'B'C' are similar. BC ra Then But B'C' r' a'' p _ BC p'~B'C'' p _r _a ~~ §424 Why? §445 478. Theorem. The area of a regular polygon is equal to half the product of the perimeter by the apothem. Given ABCDEF a regular polygon, of which A is the area, a the apothem,... | |
 | Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...vertices. Corollary. The radii of a regular polygon are equal. The apothems are equal. Theorem VII. The area of a regular polygon is equal to half the product of its perimeter by its apothem. Theorem VIII. Two regular polygons of the same number of sides are similar. Corollary 1. The... | |
 | Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...vertices. Corollary. The radii of a regular polygon are equal. The apothems are equal. Theorem VII. The area of a regular polygon is equal to half the product of its perimeter by its apothem. Theorem VIII. Two regular polygons of the same number of sides are similar. Corollary 1. The... | |
 | William Betz, Harrison Emmett Webb - Geometry, Solid - 1916 - 214 pages
...inscribed polygon. A polygon whose sides are tangent to a circle is called a circumscribed polygon. 456. The area of a regular polygon is equal to half the product of its apothem and its perimeter. 463. The circumference of a circle equals 2 TTT. 464. The length of an arc... | |
 | William Betz - Geometry - 1916 - 536 pages
...to each, other as the squares of their radii and also as the squares of their apothems. § 462 456. The area of a regular polygon is equal to half the product of its apothem and its perimeter. Given a regular polygon, with the perimeter p, the apothem r, and the area... | |
 | Fletcher Durell, Elmer Ellsworth Arnold - Geometry, Plane - 1917 - 330 pages
...segment which shall contain an angle of 45°. Of 60°. PLANE GEOMETRY. BOOK V PROPOSITION X. THEOREM 386. The area of a regular polygon is equal to half the product of its perimeter and its apothem. Given the regular polygon ABCDE with area denoted by K, perimeter by p, and apothem... | |
 | Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry - 1918 - 460 pages
...similar. § 424 BC ra Then But B'C' r' a'' p _BC p' B'C'' p _i' _a y rr=V Why? §445 Why? 478. Theorem. The area of a regular polygon is equal to half the product of the perimeter by the apothem. Given ABCDEF a regular polygon, of A which A is the area, a the apothem,... | |
 | Claude Irwin Palmer - Geometry, Solid - 1918 - 192 pages
...similar regular polygons are to each other as their radii, and also as their apothems. § 478. Theorem. The area 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... | |
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The area of a regular polygon is equal to half the product of its apothem and perimeter. 
