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Let the number of sides be n and use the formula: 1/2n(n-3) = diagonals
1/2n(n-3) = 27
Multiply both sides by 2 and then form a quadratic equation:
n2-3n-54 = 0
Solving the above quadratic equation works out as:
n = -6 or n = 9 it must be the latter because the sides can't be negative
Therefore the polygon has 9 sides.
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With 27 sides how many lines of symmetry does a polygon have?
No more than 27.
How many diagonals has a nonagon have?
It has 27 diagonals
What do you call a polygon with 27 sides?
A polygon with 27 sides is called a heptacosagon. The name is derived from the Greek words "hepta" meaning seven and "cosi" meaning twenty. The heptacosagon has 27 vertices and 27 angles, with the sum of its interior angles equal to 4050 degrees.
What is a 27 sided shpe called?
A 27-sided shape is called a heptacosagon. The prefix "hepta-" denotes the number 7, and the suffix "-gon" signifies a polygon with that many sides. Therefore, a 27-sided polygon is specifically referred to as a heptacosagon in geometry.
How many sides does a polygon have if the sum of its interior angles is 4500 degrees?
The sum of the interior angles of a polygon with n sides is (n-2)*180 degrees So (n-2)*180 = 4500 Hence n - 2 = 4500/180 = 25 and then n = 25 + 2 = 27.
How many side are there in a convex polygon having 27 diagonals?
9 sides because a nonagon has 27 diagonals
How many diagonals are in a 9 sided polygon?
The formula is: 0.5*(n2-3n) where n is the number of sides of the polygon. So: 0.5*(81-27) = 27 diagonals
What regular polygon has 27 diagonals?
It has 9 sides and it can be an regular or a irregular polygon which is called a nonagon Check: 0.5*(81-27) = 27 diagonals
How many diagonals are in a nine sided figure?
A polygon with n sides has n*(n-3)/2 diagonals. Simple as that. So a 9 sided polygon has 9*6/2 = 27 diagonals.
How many diagonals in a 9 sided polygon?
It depends. It doesn't have to always be the same shape. So it can be 0, it can be 1, as long as it has straight lines and is a closed figure, it's a polygon. * * * * * What? A polygon with n sides has n*(n-3)/2 diagonals. Simple as that. So a 9 sided polygon has 9*6/2 = 27 diagonals.
How many diagonals are there in a regular 27-gon?
In a regular polygon, the formula to calculate the number of diagonals is n(n-3)/2, where n is the number of sides. For a 27-gon, there would be 27(27-3)/2 = 351 diagonals. These diagonals are line segments that connect non-adjacent vertices of the polygon.
How many diagonals does a 30 sided polygon have?
The formula used to find the number of diagonals in a polygon is n(n-3)/2. 30 x 27/2 = 810/2 = 405 diagonals.
How many diagonals does a nine sided polygon?
For an n-sided polygon, the number of diagonals is 1+2+3+....+(n-4)+2(n-3). For a nine-sided polygon, there are 1+2+3+4+5+2(6)=27 diagonals.
With 27 sides how many lines of symmetry does a polygon have?
No more than 27.
How many sides does a polygon have if its sum totals 4500?
Assuming the sum refers to that of the interior angles, the polygon has 27 sides.
What is the formula for the number of diagonals in a nonagon?
For a 9 sided polygon it is: 0.5*(92-(3*9)) = 27 diagonals
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
