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For a regular n-sided polygon with sides of length s, the formula is:

A = (n*s^2) / (4*tan(180/n))

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How do you calculate the total degrees inside of a polygon?

By using the formula: (n-2)*180 = sum of degrees in a polygon whereas 'n' is the number of sides of the polygon


What is the formula used to calculate the number of sides in a polygon using its angle measures?

Let S be the sum of the measures of all the interior angles, in degrees. Then the number of sides is S/180 + 2.


How do you find out how many sides a shape has using the interior angle?

To find the number of sides ( n ) of a polygon using its interior angle ( A ), you can use the formula for the interior angle of a regular polygon: ( A = \frac{(n-2) \times 180}{n} ). Rearranging this equation, you get ( n = \frac{360}{180 - A} ). By substituting the known value of the interior angle ( A ), you can calculate the number of sides ( n ) of the polygon.


What is the name of 653 sides polygon?

A polygon with 653 sides is called a "653-gon." In geometry, polygons are typically named based on the number of their sides, using a numerical prefix followed by the suffix "-gon." Therefore, for a polygon with 653 sides, the naming convention directly reflects its number of sides.


What are the two ways of finding the number of sides of a polygon which has 189 diagonals?

By using the polygon diagonal formula or the quadratic equation formula in which in both formulae they work out that the polygon in question has 21 sides.


What are the steps of finding the diagonal of a polygon?

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What is the sum of the interior angles in degrees of a convex polygon with sides?

The sum of the interior angles of a convex polygon can be calculated using the formula ( (n - 2) \times 180^\circ ), where ( n ) is the number of sides in the polygon. For example, a triangle (3 sides) has a sum of ( 180^\circ ), a quadrilateral (4 sides) has ( 360^\circ ), and so on. This formula applies to any convex polygon, regardless of the number of sides.


How many sides does a regular polygon have if each angle measures 144 degrees?

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The sum of the interior angles of any polygon can be determined by using the formula (n-2)180, where n=the number of sides of that polygon. For example, you can calculate the sum of the interior angles of a polygon with five sides (a pentagon): (n-2)180 (5-2)180 3x180 540 So, the sum of the interior angles of a pentagon is 540.


How many diagonals does a 11 sided polygon have?

You can find the number of diagonals in a polygon using the formula n(n-3)/2, where n is the number of sides. Therefore an 11 sided polygon has 44 diagonals.


What is the inside angles of a polygon called?

The inside angles of a polygon are called "interior angles." The sum of the interior angles of a polygon can be calculated using the formula ( (n - 2) \times 180^\circ ), where ( n ) is the number of sides in the polygon. Each individual interior angle can be found by dividing the total sum by the number of angles (or sides) if the polygon is regular.


What is nectagon?

A nectagon is a polygon with nine sides and nine angles. It is a type of nonagon, which is a polygon with any number of sides greater than four. The sum of the interior angles of a nectagon is 1260 degrees, calculated using the formula (n-2) x 180, where n represents the number of sides.