Each side of a nonagon is 3.4 feet in length. The radius is 4.67 feet. All of the sides are equal. What is the area of the nonagon? Please show work. :) Thank you in advance :)
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It will have 9 triangles of a=3.4ft, h=4.67ft, c=4.67ft
Area of 1 triangle = 1/2(b*h)
Area of 1 Triangle = 7.939 Square Feet
Area of 9 Triangles = 71.45 square feet
Note: This method is suitable for Nonagons -Circumscribed about circle. Like this example.
For Nonagons inscribed about circle, use the following formula to calculate the area of 1 triangle
A=Square Root of(S*(S-a)*(S-b)*(S-c)), Where, S = (a+b+c)/2 (a,b,c are the lengths of the sides of triangle)
Circumscribed about circle : Radius will touch the mid point of all sides.
Inscribed about circle: Radius will touch the end points of all sides.
Area of 1 triangle = 1/2(b*h)
Area of 1 Triangle = 7.939 Square Feet
Area of 9 Triangles = 71.45 square feet
Note: This method is suitable for Nonagons -Circumscribed about circle. Like this example.
For Nonagons inscribed about circle, use the following formula to calculate the area of 1 triangle
A=Square Root of(S*(S-a)*(S-b)*(S-c)), Where, S = (a+b+c)/2 (a,b,c are the lengths of the sides of triangle)
Circumscribed about circle : Radius will touch the mid point of all sides.
Inscribed about circle: Radius will touch the end points of all sides.
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Consult: http://en.wikipedia.org/wiki/Nonagon