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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

## A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 264 pages
...homologous altitudes of similar A have the same ratio as their bases). .-.P:P'=OA:O'A'=OM:OM'. QED 414. COR. The areas of two regular polygons of the same number of sides are to each other as the squares of the radii of their circumscribed circles, and also as the squares of...

## Principles of Plane Geometry

James Wallace MacDonald - Geometry - 1894 - 76 pages
...Let 2 R represent the diameter ; the circumference will be 2irR. Proposition XIII. A Theorem. 278. The areas of two regular polygons of the same number of sides are to each other : I As the squares of their sides. ; { \tl; As the squares of the radii of circumscribed...

## Principles of Plane Geometry

James Wallace MacDonald - Geometry - 1889 - 80 pages
...II. Let 2 J? represent the diameter ; the circumference will be 2 Proposition XIII. A Theorem. 278. The areas of two regular polygons of the same number of sides are to each other : I. As the squares of their sides. Proposition XIV. A Theorem. 279. The areas of circles...

## Manual of Plane Geometry: On the Heuristic Plan, with Numerous Extra ...

George Irving Hopkins - 1891 - 208 pages
...in the same ratio as the squares of any two homologous sides. Sug. Consult 431. 494. The perimeters of two regular polygons of the same number of sides are in the same ratio as the radii of their circumscribed circles. Sug. Consult 359 and 492. 495. The perimeters of two regular...

## Manual of Plane Geometry, on the Heuristic Plan: With Numerous Extra ...

George Irving Hopkins - Geometry, Plane - 1891 - 208 pages
...same ratio as the radii of their circumscribed circles. Sug. Consult 359 and 492. 495. The perimeters of two regular polygons of the same number of sides are in the same ratio as their apothegms. 496. The areas of two regular polygons of the same number of sides are in the same...

## Arithmetic

George Albert Wentworth - Algebra - 1892 - 312 pages
...the same number of sides are proportional to their sides ; and the same is true of their apothems. The areas of two regular polygons of the same number of sides are proportional to the squares of their sides, or the squares of their radii, or the squares of their...

## "Wentworth & Hill's Exercise Manual: Arithmetic, Volume 1

George Albert Wentworth - 1894 - 320 pages
...the same number of sides are proportional to their sides ; and the same is true of their apothems. The areas of two regular polygons of the same number of sides are proportional to the squares of their sides, or the squares of their radii, or the squares of their...

## The Elements of Geometry

Webster Wells - Geometry - 1894 - 400 pages
...Then, But, Whence, AB* AW*' K' AB ^R_ A'B' ~ R' K ^ R2 _ Iff 7? '2 ~ .A. Ji (§ 320.) ,.'2 That is, 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. PROPOSITION VI. THEOREM....