 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.  Elements of Geometry - Page 170by Andrew Wheeler Phillips, Irving Fisher - 1897 - 354 pagesFull view - About this book
 | Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...of the zone generated by the arc CD = GO x 2irR. 711. Corollary 2. The areas of two spheres are to each other as the squares of their radii, or as the squares of their diameters. SUGGESTION. Let R and R' be the radii of two spheres, then 47rR2 and 4xR'J will be their... | |
 | William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 284 pages
...to each other as the squares of their radii. M' M 499. COK. 6. The areas of similar segments are to each other as the squares of their radii or as the squares of their chords. For let S and S' denote the areas of the similar As AOB and A'O'B', and K and K' the areas... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 328 pages
...§428). Then AE = OA = OF A'E' O'A' O'f (§ 435). 539. Cor. 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. Ex. 998. Two regular hexagons are inscribed in circles whose radii are 7 inches and 8 inches, respectively.... | |
 | Geometry, Plane - 1911 - 192 pages
...they are divided proportionally by the smaller circle. 6. The areas of two regular polygons of the same number of sides are to each other as the squares of their radii or their apothems. 6. Prove that if one acute angle of a triangle is double another the triangle can be... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 332 pages
...Cor. I. The area of a circle is equal HINT. K=%C- JJ = 563. Cor. n. The areas of two circles are to each other as the squares of their radii, or as the squares of their diameters. 564. Cor. m. The area of a sector whose angle is a° is #. (See §551.) Ex, 1008. Find the... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry, Modern - 1911 - 266 pages
...But P:P' = AB: A'B' = AD : A'D'. (Why ?) 407. COR. The areas of regular polygons of the same num ber of sides are to each other as the squares of their radii or apothems. Ex. 948. The lines joining the midpoints of the radii of a regular pentagon enclose a regular... | |
 | Robert Louis Short, William Harris Elson - Mathematics - 1911 - 216 pages
...From step 2, § oon BC R Then, K R2 K' Or, the areas of two similar polygons are in the same ratio as the squares of their radii, or as the squares of their apothems. THEOREM LXXVIII 284. The area of a regular polygon is equal to one half the product of its perimeter... | |
 | William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...:r: r'. §382 Why ? Why? §391 §452 Ax. 1 455. COROLLARY. 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. § 452 PROPOSITION VII. THEOREM 456. The area of a regular... | |
 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...). : r'. §382 Why? Why? §391 §452 Ax. 1 455. COROLLARY. 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. § 452 PROPOSITION VII. THEOREM 456. The area of a regular... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 490 pages
...AD:A'D'. (Why?) .'. P: P' = OD : O'D' = AO:A'0'. QBD 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 pentagon inclose a regular... | |
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