# Area of Polygons

• ### Regular Polygon

Introduction: It is often necessary to determine the dimensions of a regular polygon inscribed in or circumscribed about a given circle, or to determine the size of a circle that can be inscribed in or circumscribed about a given polygon. Such problems are readily solved by trigonometry and some of them may be solved by […]

• ### Circumscribed and Inscribed Circle

Circumscribed Circle: If a polygon is drawn in a circle so that every corner of the polygon lies on the circle, the polygon is called an inscribed polygon and the circle is called the circumscribed circle. In the figure, is the center of the polygon and is the radius of the circumscribed circle and id […]

• ### Properties of a Regular Polygon

The sides and interior angles of a regular polygon are all equal. The bisectors of the interior angles of a regular polygon meet at its center. The perpendiculars drawn from the center of a regular polygon to its sides are all equal. The lines jointing the center of a regular polygon to its vertices are […]

• ### Area of a Regular Polygon 1

Let , be the length of a side of a regular polygon of sides and be the center of the polygon. As there are sides, similar triangles are formed. Let be one of the triangles, then and Area of the regular polygon area of Area of the regular polygon But , Or Or Area of […]

• ### Area of a Regular Polygon 2

Area of a Regular polygon of n sides when the radius r of the inscribed circle is given:Since Area of the polygon area of the But , and Hence, area of the regular polygon Also, perimeter of the polygon (Putting for from above) Example: A regular octagon circumscribed a circle of radius. Find the area […]

• ### Area of a Regular Polygon 3

Area of a Regular polygon of n sides when the radius r of the circumscribed circle is given: Let be the radius of the circumscribed circle. Area of the polygon area of But Area of Also, Perimeter of the polygon But Also Perimeter Or (As) Example: A regular decagon is inscribed in a circle, the […]