 | 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... | |
 | Evan Wilhelm Evans - Geometry - 1862 - 116 pages
...triangles into which the polygon is divided. Cor. Since the area of each triangle is equal to 38 GEOMETRY. half the product of its base by its altitude, the...angles are all the angles of a quadrilateral equal tl, Of a pentagon?^ Of a hexagon ? £-Of a heptagon ? etc. j ^ 2. What is the area of a regular pentagon... | |
 | 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... | |
 | 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... | |
 | 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 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... | |
| |
The area of a regular polygon is equal to half the product of its apothem and perimeter. 
