## How do you find the diagonals of a polygon?

The number of diagonals in a polygon that can be drawn from any vertex in a polygon is three less than the number of sides. To find the total number of diagonals in a polygon, multiply the number of diagonals per vertex (n – 3) by the number of vertices, n, and divide by 2 (otherwise each diagonal is counted twice).

What polygon has 12 diagonals?

Dodecagon
How Many Diagonals are there in a Dodecagon? There are 54 diagonals in a dodecagon. These diagonals can be calculated with the help of the formula: 1/2 × n × (n-3), where n = number of sides. In this case, n = 12.

### How many diagonals are there in a polygon of 8 sides?

an octagon has 8(8−3)/2 = 8×5/2 = 20 diagonals.

Is there a polygon with 15 diagonals?

Therefore, there are 90 diagonals in a 15 sided polygon….

3 sided: 3 x 0 = 0
9 sided: 9 x 3 = 27
11 sided: 11 x 4 = 44
13 sided: 13 x 5 = 65
15 sided: 15 x 6 = 90

#### How do you calculate diagonals?

You can use the Pythagorean theorem to estimate the diagonal of a rectangle, which can be expressed with the following formula: d² = l² + w² , and now you should know how to find the diagonal of a rectangle explicit formula – just take a square root: d = √(l² + w²) .

What are diagonals of a polygon?

Polygons. As applied to a polygon, a diagonal is a line segment joining any two non-consecutive vertices. Therefore, a quadrilateral has two diagonals, joining opposite pairs of vertices.

## What polygon has 35 diagonals?

decagon
A polygon has 10 sides is known as decagon. ∴ Decagon has 35 diagonals.

What is a 100 sided polygon?

In geometry, a hectogon or hecatontagon or 100-gon is a hundred-sided polygon. The sum of all hectogon’s interior angles are 17640 degrees.

### How many diagonals are there in a Pentagon *?

So, Number of diagonals in pentagon is 5.

How many diagonals does a 50 sided polygon have?

The number of diagonals in a polygon with 50 sides is 1175.

#### How many sides does a polygon have if it has 27 diagonals?

The polygon has 9 sides.

How many sides does a polygon have if it has 135 diagonals?

Hence the number of sides of the polygon is 18.

## How to calculate the number of diagonals in a polygon?

Ans: We know that, number of diagonals in a polygon = n ( n – 3) 2. In a 20 -sided polygon, the total diagonals are = 20 ( 20 – 3) 2 = 170. But, since one vertex does not send any diagonals, the diagonals by that vertex must be subtracted from the total number of diagonals.

How many diagonals does a square have in it?

1 a square (or any quadrilateral) has 4 (4−3)/2 = 4×1/2 = 2 diagonals 2 an octagon has 8 (8−3)/2 = 8×5/2 = 20 diagonals. 3 a triangle has 3 (3−3)/2 = 3×0/2 = 0 diagonals.

### How to calculate the number of sides of a hexadecagon?

As we know, the total number of sides of a hexadecagon is x. Substituting the values in the formula of diagonal of polygon we get, As the value of x cannot be negative. Hence, the number of sides of a polygon with 90 diagonals is 15. The number of sides of a polygon with 90 diagonals = 15.

How many diagonals are there in a pentagon?

There are five diagonals in a pentagon, whether regular or irregular and nine diagonals in a hexagon. Diagonals will always be within the interior of convex, simple polygons. Consider the shape of a rectangular door. A line can be drawn from the top hinge corner to the bottom hinge corner on the opposite side.