| George Roberts Perkins - Geometry - 1860 - 472 pages
...FOURTH BOOK. DETERMINATION OF THE SIDES AND OF THE AREAS OF REGULAR POLYGONS. THEOREM V. The area of any **regular polygon is equal to half the product of its perimeter by its** apothem. For, the equal isosceles triangles OAB, " OBC, OCD, etc., give OAB = AB x \ of OG, OBC=BCxiof... | |
| Adrien Marie Legendre - Geometry - 1863 - 464 pages
...the decagon, we may construct regular polygons of 20, 40, 80, &c., sides. PEOPOSITION VIII. THEOREM. **The area of a regular polygon is equal to half the product of its perimeter** and apothem. Let GHIK be a regular polygon, O its centre, and OT its apothem, or the radius of the... | |
| William Chauvenet - Geometry - 1871 - 380 pages
...1, n being an integer, provided that 2" -j- 1 is a prime number. PROPOSITION VIII.— THEOREM. 22. **The area of a regular polygon is equal to half the product of its perimeter** and apothem. For, straight lines drawn from the centre to the vertices of the polygon divide it into... | |
| William Chauvenet - Geometry - 1871 - 380 pages
...1, n being an integer, provided that 2™ -(- 1 is a prime number. PROPOSITION VIII.— THEOREM. 22. **The area of a regular polygon is equal to half the product of** Us perimeter and apothem. For, straight lines drawn from the centre to the vertices of the polygon... | |
| Charles Davies - Geometry - 1872 - 464 pages
...decagon, .we may construct regular polygons of 20, 40, 80, >tc., sides. PROPOSITION VIII. THEOREM. **The area of a regular polygon is equal to half the product of its perimeter** and apothem. • Let G'HIK be a regular polygon, 0 its centre, and OT its apothem, or the radius of... | |
| William Chauvenet - Mathematics - 1872 - 382 pages
...1, 11 being an integer, provided that 2" -f 1 is a prime number. PROPOSITION VIII.— THEOREM. 22. **The area of a regular polygon is equal to half the product of its perimeter** and apothem. For, straight lines drawn from the centre to the vertices of the polygon divide it into... | |
| William Frothingham Bradbury - Geometry - 1872 - 262 pages
...sides are as their apothems ; and the polygons as the squares of their apothems. THEOREM 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 composed is equal to half the product... | |
| William Frothingham Bradbury - Geometry - 1873 - 132 pages
...sides are as their apothems ; and the polygons as tlie squares of their apothems. THEOREM 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 composed is equal to half the product... | |
| Adrien Marie Legendre - Geometry - 1874 - 500 pages
...the decagon, we may construct regular polygons of 20, 40, 80, &c., sides. PROPOSITION Vin. THEOREM. **The area of a regular polygon is equal to half the product** qf its perimeter and apothem. Let GHI1T be a regular polygon, 0 its centre, and OT its apothem, or... | |
| William Chauvenet - Geometry - 1875 - 466 pages
...+ 1, n being an integer, provided that 2" -j- 1 is a prime number. PROPOSITION VIII.—THEOREM. 22. **The area of a regular polygon is equal to half the product of** Us perimeter and apothem. For, straight lines drawn from the centre to the vertices of the polygon... | |
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