Exploring Decagon | Properties, Formulas, and Calculations

Decagon

A decagon is a polygon with ten sides and ten angles

A decagon is a polygon with ten sides and ten angles. The word “decagon” is derived from the Latin terms “decem,” meaning ten, and “gonia,” meaning angle. In a regular decagon, all sides are equal in length and all angles are equal, measuring 144 degrees.

To find the sum of the interior angles of a decagon, you can use the formula:
Sum of interior angles = (n-2) * 180 degrees
where n is the number of sides of the polygon. So for a decagon, the sum of interior angles would be (10-2) * 180 = 8 * 180 = 1,440 degrees.

The formula for finding the measure of each interior angle of a regular decagon is given by:
Measure of each interior angle = Sum of interior angles / Number of sides
So, for a regular decagon, each interior angle would be 1,440 degrees / 10 = 144 degrees.

The formula for finding the measure of each exterior angle of a regular decagon is given by:
Measure of each exterior angle = 360 degrees / Number of sides
Therefore, for a regular decagon, each exterior angle would be 360 degrees / 10 = 36 degrees.

To calculate the area of a regular decagon, you can use the formula:
Area = (1/4) * (s^2) * n * cot(180/n)
where s is the length of the sides and n is the number of sides. For a regular decagon, since all sides are equal, you can simplify it to:
Area = (5/4) * s^2 * cot(36 degrees)
In this formula, cot(36 degrees) represents the cotangent of 36 degrees. You can use a calculator to find its decimal value and substitute it in the formula along with the value of s to find the area of a regular decagon.

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