Construction and Finding the Area of the New Geometric Figure, n-cardioid

This paper is an original and basic research that will give the definition, the process of construction and the formula for finding the area of a new geometric figure formed on a mathematical problem of a goat tied in the corner of a shed. This new geometric figure was named as n-cardiod. The n- cardiois is the union of the arciX formed when a tension that measures half of the polygons perimeter is tied at any vertex of closednP and is rotated in a clockwise and counter clockwise direction until it touches the polygon, wherenP is a regular polygon with verticesnxxx ,…,, 21 , n sides and length of sides s for alln . The area of the n-cardioid will be solved using the formula2 2 24 45 s n A         .

Keywords – n-cardioid, polygons, arc, area.