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# When all the diagonals are drawn from one vertex of an octagon?

## When all the diagonals are drawn from one vertex of an octagon?

Answer Expert Verified Thus for each of the 8 vertices you can draw 5 diagonals and hence you have constructed 5 8 = 40 diagonals. But you have constructed each diagonal twice, once from each of its ends. Thus there are 20 diagonals in a regular octagon.

## How many diagonals can be formed in an octagon if only one vertex is the reference point?

Count the diagonals. For the square, there are two diagonals: one diagonal for every two vertices. A hexagon has 9 diagonals: there are three diagonals for every three vertices. An octagon has 20 diagonals.

How do you find the diagonal of a octagon?

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

### How many diagonals can be drawn from vertex A?

5 diagonals
You cannot draw diagonals to the vertex itself as well as two adjacent vertices and hence you can draw 5 diagonals from the vertex.

### How many diagonals can be drawn from a vertex of a triangle?

This can easily be proved by the congruence of alternate interior angles. From a given vertex of a polygon with n sides, (n-3) diagonals can be drawn. Every diagonal drawn from a single vertex of a polygon creates one triangle within the polygon, except for the last diagonal, which creates two triangles.

What is the formula to find diagonals?

The formula to calculate the number of diagonal of an n-sided polygon = n(n-3)/2 where n is the number of sides of the polygon.

## What is the diagonals from a fixed vertex?

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).

## How do you calculate diagonals?

You can find the diagonal of a rectangle if you have the width and the height. The diagonal equals the square root of the width squared plus the height squared.

How many diagonals are in a Heptagon?

14 diagonals
Heptagon is a polygon ( a closed shape made up of line segments) made up of 7 sides and 7 angles. The word heptagon is made up of two words, hepta meaning seven and gon meaning sides. There are 14 diagonals in a heptagon and in the given heptagon, the blue line segments represent the diagonals.

### What is the diagonal of a triangle?

A diagonal of a polygon is a line from a vertex to a non-adjacent vertex. So a triangle, the simplest polygon, has no diagonals. You cannot draw a line from one interior angle to any other interior angle that is not also a side of the triangle. A quadrilateral, the next-simplest, has two diagonals.

How many diagonals can you draw from a vertex in an octagon?

In a regular octagon, from a vertex you can only draw 5 diagonals. A line from a vertex to the next adjacent vertex on either side is not a diagonal. . Let’s use something you are familiar with. If you are given a square (which has four sides and is a quadrilateral), how many diagonals can you draw from one corner? The answer

## How many lines are there in a regular octagon?

a regular octagon has 8 vertices; so from one vertex, lines can be drawn to the other 7 vertices. the lines to the two adjacent vertices are sides of the octagon the other 5 lines are diagonals.

## How many diagonals can you draw from one corner of a square?

If you are given a square (which has four sides and is a quadrilateral), how many diagonals can you draw from one corner? The answer is 1 diagonal from that corner, not 4 – 1 = 3. From one vertex in a square the only diagonal you can draw is from that vertex to the vertex in the opposite corner.

What is the probability of selecting the longest diagonal in an octagon?

Thus if you select one diagonal from all the diagonals in a regular octagon there are 4 chances in 20 that you will select one of the longest ones, and hence a probability of 4 / 20 = 1 / 5. What about the shortest?