A Polygon Has 54 Diagonals How Many Sides

N n 1 2 n. Diag nn - 32.

Prove Number Of Diagonals Of A Polygon Youtube

Next multiply that number by the number of sides.

. Only positive solution for n will be n 20. So the polygon has 12 sides and it is a dodecagon. So nn-3 2 170.

In fact it is the polygon with the least number of sides. Using this formula we are going to relate that is to equate the number of diagonals given and the formula by equating we can solve and. Plugging in the known information we know that diag 54.

Lets try a polygon with 10 sides and see what we get. So total diagonals will be nn-3 2. The formula for the number of diagonals that can be formed in a polygon with n sides is.

By using the formula for the number of diagonals of a polygon with n sides you can determine how many sides a polygon has if you know the number of diagonals it has. How many diagonals does a 20-sides polygon have. So your polygon has 20 sides vertices.

The no of sides in a polygon is 12 and this polygon is called dodecagon. Number of diagonal in a polygon having n side is 2 n n 3 5 4 given n n 3 5 4 2 1 0 8 1 2 9 n 1 2 Was this answer helpful. If in a regular polygon the number of diagonals is 54 then the number of sides of this polygon is.

Number of line segments obtained by joining the vertices of an n sided polygon taken two at a time Number of ways of selecting 2 out of n n C 2 2 n n 1. These shapes have seven 13 70 and 672 sides respectively. Divide by two comes because otherwise we will be counting each diagonal twice.

Some other polygons are the heptagon the tridecagon the heptacontagon and the hexahectaheptacontakaidigon. Can you make a polygon with only 2 sides. If in a regular polygon the number of diagonals is 54 then the number of sides of this polygon is.

Nn 32 77. Given that this is equal to 27 we have that n n322754. Number of all connections between all the vertices N n n 1 2 Thus number of diagonals N n n n 1 2 n n n 1 2 2 n n 3 2 But actual given number of diagonals 27 Therefore n n 3 2 27.

A polygon of n sides has. Finally divide the answer by 2 and youll have the number of diagonals within the polygon. N n-32 54 or.

Lets use this formula now for a polygon with a larger number of sides. A polygon with n sides had nn-32 diagonals. For example they call the hexahectaheptacontakaidigon a 672-gon.

Now you could just try values of n until you find one that works shouldnt take too long or you could solve the quadratic equation if you know how to do that. N n-3 108 or. See sol in pic.

Then there are n sides. For polygons with more than 10 sides many mathematicians use the more manageable n-gon form. If in a regular polygon the number of diagonals is 54 then the number of sides of this polygon is.

A triangle is a three-sided polygon. N2 - 3n - 340 0. Nn 32 D where n number of sides D total number of diagonals in the polygon.

How many sides has a polygon with 54 diagonals. N C 2 n n 1 2. N-12 n9 0 so n 12.

Remember the formula is. Then subtract 3 from the number of sides. So a 20 sided polygon would have 20173 170.

So the number of diagonals of a polygon of. N -9 is inadmissible. If in a regular polygon the number of diagonals is 54 then the number of sides of this polygon is.

A polygon of n sides has. A polygon of n sides has nn-32 diagonals. How many sides are there if a polygon has 54 diagonals.

What is the minimum number of sides in a polygon. For example if a polygon has 6 sides youd find it has 9 diagonals. Let n be the number of vertices of the polygon.

N n - 3 2 diagonals. Find the number of its sides. A polygon with 10 sides has 35 diagonals.

In geometry a digon is a polygon with two sides edges and two vertices. So for a polygon with n 12 there are 54 diagonals. For an alternate way to determine the number of diagonals in a polygon read on.

A polygon has 54 diagonals. N n - 3 2 diagonals. The diagonals of any poygon can be calculated using the formula n2 n3 where n is the number of sides in case of a pentagon which n.

Since there are 54 diagonals. The number of diagonals of a polygon of n sides is given by n n-32. Yes the more sides you have the more diagonals you have and the number of diagonals grows quite quickly at that too.

For example if a polygon has 54 diagonals find how many sides it has. By joining any two vertices of a polygon we obtain either a side or a diagonal of the polygon. Sides are given by.

It must have 15 sides to comply with the formula- 05152-315 90 diagonals So. How many diagonals does a convex polygon with 23 sides have. If a polygon has n sides vertices then there can be n-3 diagonals emanating from a vertex.

N23n-108 0 or. 1010 - 32 1072 702 35. 36015 24 degrees and 180-24 156 degrees.

The number of diagonals in any polygon is n n32. N 2 3 n 54 n 2 3 n 54 0 n 2 9 n 6 n 54 0 n n 9 6 n 9 0 n 9 n 6 0.

Diagonals Of A Polygon Formula Examples