 | Isaac Sharpless - Geometry - 1882 - 286 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 one.. half 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+FC+ CG+ GH +HA)ED.... | |
 | George Albert Wentworth - Geometry - 1890 - 296 pages
...diameter is 2 R and circumference C, we have ^ = TT, or C=2*R. PROPOSITION VIII. THEOREM. 421. The area of a regular polygon is equal to one' half the product of its apothem by its perimeter. E AMB Let P represent the perimeter, R the apothem, and S the area of the... | |
 | Henry Holmes Belfield - Arithmetic - 1891 - 362 pages
...of a polygon is equal to the sum of the areas of the triangles into which it is divided. Hence. /'he area of a regular polygon is equal to one half the product of the perimeter of its base and its altitude. Find the area of the following regular polygons : 1. A... | |
 | George Albert Wentworth - Geometry, Plane - 1892 - 266 pages
...any circle whose diameter is 2 R and circumference C, we have C PROPOSITION VIII. THEOREM. 421. The area of a regular polygon is equal to one. half the product of Us apothem by Us perimeter. ED A. HB Let P represent' the perimeter, R the apothem, and 8 the area... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 522 pages
...When will there be two solutions, when one solution, and wb^n no soluPROPOSITION IX. THKORBM. 309. The area of a regular polygon is equal to one half the product of its perimeter and apothem. Let A BC DEF be a regular polygon, and O JT itt To prove that the area of the polygon equals one half... | |
 | Middlesex Alfred Bailey - Arithmetic - 1897 - 332 pages
...trapezoid is equal to one half the product of the sum of its parallel sides by its altitude. VIII. The area of a regular polygon is equal to one half the product of its perimeter by its apothem. IX. The area of a circle is equal to the square of its radius times 3.1416. X. The... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...apothems. Use a method of proof similar to that used in Prop. 199. Proposition 2O1. Theorem. 238. The area of a regular polygon is equal to one half the product of its perimeter and apothem. Draw the radii of the polygon, and consult Prop. 166. Proposition 2O2. Problem. 239. To inscribe a... | |
 | William James Milne - Geometry, Modern - 1899 - 258 pages
...(AB + BC+ etc.) • OF ; that is, ABCDE =0= J rect. P • OF. Therefore, etc. QED 389. Cor. I. The area of a 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... | |
 | William James Milne - Geometry - 1899 - 398 pages
...(AB + Bc -f etc.) . OF ; that is, ABCDE =0= J rect. P • OF. Therefore, etc. QED, 389. Cor. I. The area of a 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 <ire to each other as the... | |
 | Adelia Roberts Hornbrook - Arithmetic - 1900 - 428 pages
...triangles as it has sides, we may find the area of a regular polygon by the following principle: The area of a regular polygon is equal to one half the product of its perimeter and apothem. What is the area of a regular pentagon if the perimeter is 80 in. and the apothem 10.88 in. ? 91. The... | |
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The area of a regular polygon is equal to one half the product of its apothem and perimeter. 
