 Prove two of the following propositions: The work may be limited to drawing a figure and giving a synopsis of the demonstration. (a) If the area of a regular polygon is equal to the product of the perimeter by one-half the apothem, it follows that the...  Plane Geometry - Page 218by George D. Pettee - 1896 - 253 pagesFull view - About this book
 | Adrien Marie Legendre - Geometry - 1819 - 574 pages
...be inscribed, within a circle, all the polygons that can be circumscribed about it. THEOREM. £80. The area of a regular polygon is equal to the product of its perimeter by /to// of the radius of the inscribed tirde. Demonstration. Let there be, for example,... | |
 | Adrien Marie Legendre - 1825 - 570 pages
...may be inscribed, within a circle, all the polygons that can be circumscribed about it. THEOREM. 230. The area of a regular polygon is equal to the product of its perimeter by half of the radius of the inscribed circle. Demonstration. Let there be, for example,... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...may be inscribed, within a circle, all the polygons that can be circumscribed about it. THEOREM. 280. The area of a regular polygon is equal to the product of its perimeter by half of the radius of the inscribed circle. Demonstration. Let there be, for example,... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 pages
...may be inscribed, within a circle, all the polygons that can be circumscribed about it. THEOREM. 280. The area of a regular polygon is equal to the product of its perimeter by half of the radius of the inscribed circle. Demonstration. Let there be, for example,... | |
 | Timothy Walker - Geometry - 1831 - 166 pages
...triangles, its area must be C Exhalf of A Df C EX half of BC, or C Exhalf of (A B+BC). 104. THEOREM.— The area of a regular polygon is equal to the product of its perimeter by half the radius 6 F 64 of the inscribed circle. Let ABCDEF (fig. 64) be the polygon,... | |
 | Etienne Bézout - Calculus - 1836 - 216 pages
...given circle. We here also may consider the curve as a regular polygon of a great number of sides. The area of a regular polygon is equal to the product of its perimeter, by half of the perpendicular let fall from the centre upon one of the sides. Therefore... | |
 | Etienne Bézout - Calculus - 1836 - 218 pages
...given circle. We here also may consider the curve as a regular polygon of a great number of sides. The area of a regular polygon is equal to the product of its perimeter, by half of the perpendicular let fall from the centre upon one of the sides. Therefore... | |
 | Henry Bartlett Maglathlin - Arithmetic - 1869 - 332 pages
...is equal to the triangle WXZ plus the triangle XYZ, made by __ / _ I^lv *ke diagonal X Z. W J\. 5. The area of a REGULAR POLYGON is equal to the product of the perimeter by half the perpendicular drawn from the center to any one of the sides. For, any regular polygon, ABCDEF,... | |
 | Henry Bartlett Maglathlin - 1871 - 336 pages
...the trapezium WXYZ is equal to the triangle WXZ plus the triangle XYZ, made by the diagonal X Z. 5. The area of a REGULAR POLYGON is equal to the product of the perimeter by half the perpendicular drawn from the center to any one of the sides. For, any regular polygon, ABCDEF,... | |
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