...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...

...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...

....-.R—lim.(r) = Q. §199 .'. lim. (r) = R. BEGULAR POLYGONS AND CIRCLES. PROPOSITION IX. THEOREM. 379. The area of a regular polygon is equal to one-half the product of its apothem by its perimeter. E D Let P represent the perimeter and R the apothem of the regular polygon ABC, etc....

...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...

...and denote its perimeter by P, and its apothegm by r. Then the area of this polygon = J r XP, § 379 (the area of a regular polygon is equal to one-half the product of its apothegm by the perimeter). Conceive the number of sides of this polygon to be indefinitely increased,...

...polygon, and denote its perimeter by P, and its apothem by r. Then the area of this polygon =£rXP, §379 (the area of a regular polygon is equal to one-half the product of Us apothem by the perimeter). Conceive the number of sides of this polygon to be indefinitely increased,...

...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...

...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...

...."". 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...

...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...