| Edward Olney - Geometry - 1872 - 472 pages
...equals altitude into |(AB + DC), = altitude into ab. QED FIG. 228. PROPOSITION raí. 326. Theorem. — **The area of a regular polygon is equal to onehalf the product of its apothem** into its perimeter. DEM. — Let ABCDEFC be a regular polygon whose apothem is Oa; then is its area... | |
| Edward Olney - Geometry - 1872 - 566 pages
...altitude into i (AB + DC), — altitude into ab. q. ED Fra. PROPOSITION VIII. 326. Ttieorem. — T/ie **area of a regular polygon is equal to onehalf the product of its apothem** into its perimeter, DEM. — Let ABCDEFC be a regular polygon whose apolhem is Oa; then is its area... | |
| Edward Olney - Geometry - 1877 - 272 pages
...altitude into i(AB + DC), = altitude into ab. QED n- B FIG. 228. PROPOSITION VIII. 326. Theorem.—The **area of a regular polygon is equal to onehalf the product of its apothem** into its perimeter. DEM.—Let ABCDEFC be a regular polygon whose apothem is Oa; then is its area equal... | |
| Isaac Sharpless - Geometry - 1879 - 282 pages
...polygons of 12, 24, etc.; from a pentedecagon, figures of 30, 60, etc. Proposition 9. Theorem.—The **area of a regular polygon is equal to onehalf the product of its** perimeter and apothem. Let ABC be a polygon and DE its apothem; then the area of AB C is equal to $(AB+BF... | |
| George Albert Wentworth - 1881 - 266 pages
...polygon, and denote its perimeter by P, and its apothem by r. Then the area of this polygon = lr XP, **§379 (the area of a regular polygon is equal to one-half the product of its apothem by** the perimeter). Conceive the number of sides of this polygon to be indefinitely increased, the polygon... | |
| George Albert Wentworth - Geometry, Plane - 1882 - 268 pages
...assigned quantity. .-. Um. (R — r) = 0. .-.R — lim.(r) = Q. §199 .-.lim. (r) = R. a. ED REGULAR **POLYGONS AND CIRCLES. PROPOSITION IX. THEOREM. 379....regular polygon ABC, etc. We are to prove the area of** ABC, etc., = \ RX P. Draw 0 A, OB, 0С, etc. The polygon is divided into as many A as it has sides.... | |
| George Albert Wentworth - Geometry, Plane - 1879 - 250 pages
...than any assigned quantity. ."". Urn. (R — r) = Q. .-.R—lim.(r) = 0. §199 .-. lim. (r) = R. QED **PROPOSITION IX. THEOREM. 379. The area of a regular polygon is equal to one-half the product of** Us apothegm by its perimeter. B ED Let P represent the perimeter and R the apothegm of the regular... | |
| Edward Olney - Geometry - 1883 - 354 pages
...DC) ; and area ABCD. which equals £ (AB + DC) x IK, = ab x IK. QED PROPOSITION IX. 351. Theorem. — **The area of a regular polygon is equal to one-half the product of its apothem** into its perimeter. DEMONSTRATION. Let ABCDEFG be a regular polygon, whose perimeter is AB + BC + CD... | |
| Edward Olney - Geometry - 1883 - 344 pages
...opposite. Whence Km = oD. In like manner, we may show that Cp = nB. PROPOSITION IX. 351. Theorem.—The **area, of a regular polygon is equal to one-half the product of its apothem** into its perimeter. DEMONSTRATION. Let ABCDEFG be a regular polygon, whose perimeter is AB + BC + CD... | |
| George Albert Wentworth - Arithmetic - 1886 - 372 pages
...trapezoids thus formed, and their sum will be the area required of the polygon. FIG. 47. 425. THEOREM. **The area of a regular polygon is equal to one-half the product of its** perimeter by its apothem. Thus, in the regular octagon ABC, etc., if we draw from the centre O lines... | |
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