PENTAGON

(Gr. van, and yu>v,a, angle.) In Geometry, a plane figure, having five angles, or contained by five sides. It is a rtgiilar pentagon when the sides and angles are equal, and is consequently inscribable in a circle. The length of the side of a regular pentagon is equal to twice the sine of 36°, radius being unit; and its area= 3 sin. 36° X cos. 36°; or, making the side = s, the area = | si X tan. 54°. It is a remarkable property of the regular pentagon, that the square of its side is equal to the sum of the squares of the sides of the hexagon and decagon inscribed in the same circle. [s. 929]