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How do you find the number of sides a polygon has when it has 27 diagonals?
Let the number of sides be x and use the diagonal formula:- 1/2*(x2-3x) = 27 Multiply both sides by 2: x2-3x = 54 Subtract 54 from both sides: x2-3x -54 = 0 Using the quadratic equation formula gives x a positive value of 9 So the polygon has 9 sides which is a nonagon
What are the number of diagonals for a regular polygon with 12 sides?
It is: 0.5*(144-36) = 54 diagonals
How many sides does an n-gon have?
An n-gon is the generic name for a polygon with nsides. It is an especially useful name for a polygon with a number of sides such that giving the polygon a name becomes complicated. For example, calling a shape with 54 sides a 54-gon is much simpler than calling the same shape a pentacontakaitetragon.
How many sides does the polygon have interior angles sum to 9360?
To find the number of sides ( n ) of a polygon where the sum of the interior angles is 9360 degrees, you can use the formula for the sum of the interior angles: ( S = (n - 2) \times 180 ). Setting this equal to 9360 gives the equation ( (n - 2) \times 180 = 9360 ). Solving for ( n ) yields ( n - 2 = 52 ), so ( n = 54 ). Thus, the polygon has 54 sides.
How many sides does a polygon have if the interior angles add up to 9360?
To find the number of sides ( n ) of a polygon based on the sum of its interior angles, you can use the formula: [ \text{Sum of interior angles} = (n - 2) \times 180 ] Setting this equal to 9360, we have: [ (n - 2) \times 180 = 9360 ] Solving for ( n ): [ n - 2 = \frac{9360}{180} = 52 \quad \Rightarrow \quad n = 54 ] Thus, the polygon has 54 sides.
What is the name of a polygon that has 54 diagonals?
It is a dodecagon which has 12 sides Check: 0.5*(144-36) = 54 diagonals
What is the name of a 54 sided polygon?
A 54-sided polygon is called a pentacontakaitetragon. In geometry, the prefix "penta-" refers to five, "conta-" refers to ten, and "kaitetra-" means four, together forming the name for a polygon with fifty-four sides.
How many sides does a regular polygon have when it has 54 diagonals?
Suppose the polygon has n sides. Then n*(n-3)/2 = 54 or n*(n-3) = 108 and so, by inspection, n = 12 or you can multiply out the brackets and solve the quadratic equation in n.
What kind of polygon has 54 diagonals?
A polygon with n sides has n*(n-3)/2 diagonals.So you need to solve n*(n-3)/2 = 54n2 - 3n - 108 = 0 which has the solutions n = 12 or n = -9.Since a polygon cannot have a negative number of sides, the answer is 12.A polygon with n sides has n*(n-3)/2 diagonals.So you need to solve n*(n-3)/2 = 54n2 - 3n - 108 = 0 which has the solutions n = 12 or n = -9.Since a polygon cannot have a negative number of sides, the answer is 12.A polygon with n sides has n*(n-3)/2 diagonals.So you need to solve n*(n-3)/2 = 54n2 - 3n - 108 = 0 which has the solutions n = 12 or n = -9.Since a polygon cannot have a negative number of sides, the answer is 12.A polygon with n sides has n*(n-3)/2 diagonals.So you need to solve n*(n-3)/2 = 54n2 - 3n - 108 = 0 which has the solutions n = 12 or n = -9.Since a polygon cannot have a negative number of sides, the answer is 12.
How many diagonals to a dodecagon?
A polygon with n sides has 1/2*n*(n - 3) diagonals. So, for a polygon, with n = 12, there are 54 diagonals.
How many diagonals can you draw in a 12 sided regular polygon?
infiniteImproved Answer:-The formula is: 0.5*(n2-3n) where n is the number of sides of the polygonSo: 0.5*(144-36) = 54 diagonals
If in a 54 sided polygon all possible diagonals are drawn from one vertex they divide the interior of the polygon into how many regions?
In a 54-sided polygon, 53 possible diagonals can be drawn from one vertex to another. These diagonals will not intersect. Therefore, the interior will be divided into 54 regions by the 53 diagonals plus the two sides of the original polygon that adjoin the vertex from which the diagonals are drawn.
