...regular polygon is equal to one half the product of its perimeter by its apothem. 390. Cor. II. Regular polygons of the same number of sides are to each other as the squares upon their radii and also as the squares upon their apothems. §§ 386, 345 Ex. 645. The sides of a...

...For nip is the area of a great O. (?) 673. Cor. V. The areas of the surfaces of two spheres are to each other as the squares of their radii, or as the squares of their diameters. (The proof is left to the pupil ; compare § 372.) EXERCISES. 22. Find the area of the surface...

...IV. Regular polygons of the same number of sides are similar. THEOREM V. 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 ; and their areas are...

...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 same number of...

...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 same number of...

...it. We have S=jr.R2 Th. 10. Whence, S = n ( JD) 2 = kn D 2. COR. 2. — The arena of circles are to each other as the squares of their radii or as the squares of their diameters. Let S and R and .S" and R' denote respectively the areas and radii of two circles. Then,...

...perimeters are in the same ratio as the apothems. The same holds true for the radii. 352. COROLLARY III. The areas of two regular polygons of the same number of sides are in the same ratio as the squares of their radii, or as the squares of their apothems. (Art. 315.) EXERCISES...

...But P:P' = AB:^'B' = AD:.4'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...

...points and from a given straight line. When is it impossible to do so ? Q. Prove that the perimeters of two regular polygons of the same number of sides are to one another as the radii of their circumscribing circles. Prove that in a given circle the perimeter...

...total areas, of two similar cones of revolution are to each other as the squares of their altitudes, as the squares of their radii, or as the squares of their slant heights ; and their volumes are to each other as the cubes of their altitudes, as the cubes of...