how do you find the surface area for a septagon??
1 Answer
flbyrne | (Level 3) Assistant Educator
A septagon is another name for a heptagon, a polygon with seven sides and seven angles. The sum of a polygon's interior angles is equal to (n-2)x`pi/2` , where n is the number of sides in the polygon, 7 for the heptagon or septagon. Therefore the sum of the interior angles for a heptagon is equal to:
Sum of interior angles=`(7-2)*(pi)=5pi`
Divide the sum of interior angles by the number of angles (7) to determine the measure of each angle:
Measure of each angle= `(5pi)/7`
The area of a regular heptagon with side a is equal to:
`A=7/4a^2cot(pi/7)=3.633912444a^2`
If the heptagon is not regular, you would need to add the areas of the 7 triangles formed by the radii.