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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
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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - Geometry - 1872 - 262 pages
...As the triangles 0 AB, 0 BC, 0 CD, &c. are equal, their altitudes are equal, that is, the bases are equidistant from the vertex 0. 35. Scholium. 0 is...XVIII. 37. The area of a regular polygon is equal to half the product of its perimeter and apothem. For the area of each triangle of which the polygon is...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 pages
...or CD : C'D', etc. Therefore the polygons fulfill the two conditions of similarity. 10. 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;...
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A Treatise on Special Or Elementary Geometry

Edward Olney - Geometry - 1872 - 472 pages
...sides are to each other as the corresponding diagonals (35O), p : P : : r : HQED , .g,370. COR. 1. — The perimeters of regular polygons of the same number of sides are to each other as the apothems of the polygons. For the apothems are to each other as the sides of the...
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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - Geometry - 1873 - 288 pages
...bases are equidistant from the vertex 0. 35. Scholium. 0 is called the centre, and the perpendicular OG the apothem of the polygon. 36. Corollary. In regular...of regular polygons of the same number of sides are аt their apothems ; and the polygons as the squares of their apothems. THEOREM XVIII. 37. The area...
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Catalogue - Harvard University

Harvard University - 1874 - 668 pages
...impossible ! Why ? Given any curve, to ascertain whether it is the arc of a circle or not. 6. Prove that the perimeters of regular polygons of the same number of sides are proportional to the iliiimeiers of their inscribed or circumscribed circles. Go on to prove that the...
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Harvard Examination Papers

1875 - 256 pages
...impossible 1 Why 1 Given any curve, to ascertain whether it is the arc of a circle or not. 6. Prove that the perimeters of regular polygons of the same number of sides are proportional to the diameters of their inscribed or circumscribed circles. Go on to prove that the...
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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...Scholium. 0 is called the centre, 0 B the radius, and the perpendicular 0 G the apothem of the polygon. 84. Corollary. In regular polygons of the same number...polygons as the squares of their apothems. THEOREM XXXVII. 85. The area of a regular polygon is equal to half the product of its perimeter and apothem....
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A Treatise on Special Or Elementary Geometry

Edward Olney - Geometry - 1882 - 262 pages
...homologous sides are to each other as the corresponding diagonals (350), p : P : : r : RQED 370. COR. 1. — The perimeters of regular polygons of the same number of sides are to each other as the apothems of the polygons. For the apothems are to each other as the sides of the...
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Elementary Geometry: Including Plane, Solid and Spherical Geometry : with ...

Edward Olney - Geometry - 1886 - 348 pages
...the homologous sides are to each other as the corresponding diagonals (387), pr 416. COROLLARY 1. — The perimeters of regular polygons of the same number of sides are to each other as the apothems of the polygons (382)417. COROLLARY 2. — The circumferences of circles...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...inscribed in it. PROPOSITION III. Regular polygons of the same number of sides are similar. 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 ;...
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