doi: **10.7392/openaccess.23050450**

Asmara College of Health Sciences, Asmara, Eritrea

Area of a circle and regular polygon i.e. including inscribed and circumscribed regular polygons are interrelated to each other. The objective is to show how the area of a circle and regular polygons is interrelating. Depend on this; these entire theorems can give an infinite ways to calculate area of a circle and other new ways for regular polygons. The methodology used is the previous known formulas for a circle and regular polygons, to derive new relation formulas. The results obtained are in relationship of a circle with regular polygons of the same perimeter, its inscribed and circumscribed regular polygons. These theorems (results) have overcome some limitations of previous existed formulas; now no need to calculate radius for a circle if only circumference is given and no use of trigonometry (sine, tangent and cosine) for regular polygons in addition to these it also brings us to a simple new way for calculating area of a sector and segment which are present in inscribed regular polygons. Therefore here are new ways for calculating area of a circle, regular polygons, segment and sector.

**Keywords: **area, circle, regular polygons, inscribed regular polygons, circumscribed regular polygons.

Citation: Dawit, G. (2013). Gabriel’s Theorems on Area of a Circle and Regular Polygons. *Open Science Repository Mathematics*, Online(open-access), e23050450. doi:10.7392/openaccess.23050450

Received: November 1, 2013

Published: November 7, 2013

Copyright: © 2013 Dawit, G. Creative Commons Attribution 3.0 Unported License.

Contact: research@open-science-repository.com

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**APA**

Dawit, G. (2013). Gabriel’s Theorems on Area of a Circle and Regular Polygons. *Open Science Repository Mathematics*, Online(open-access), e23050450. doi:10.7392/openaccess.23050450

**MLA**

Dawit, Gabriel. “Gabriel’s Theorems on Area of a Circle and Regular Polygons.” *Open Science Repository Mathematics* Online.open-access (2013): e23050450.

**Chicago**

Dawit, Gabriel. “Gabriel’s Theorems on Area of a Circle and Regular Polygons.” *Open Science Repository Mathematics* Online, no. open-access (November 07, 2013): e23050450. doi:10.7392/openaccess.23050450.

**Harvard**

Dawit, G., 2013. Gabriel’s Theorems on Area of a Circle and Regular Polygons. *Open Science Repository Mathematics*, Online(open-access), p.e23050450.

**Science**

1. G. Dawit, Gabriel’s Theorems on Area of a Circle and Regular Polygons, *Open Sci. Repos. Math*. **Online**, e23050450 (2013).

**Nature**

1. Dawit, G. Gabriel’s Theorems on Area of a Circle and Regular Polygons. *Open Sci. Repos. Math*. **Online**, e23050450 (2013).

Research registered in the DOI resolution system as:** ****10.7392/openaccess.23050450**.

This work is licensed under a Creative Commons Attribution 3.0 Unported License.