Q&A for How to Find How Many Diagonals Are in a Polygon

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What is the formula to find the number of diagonals?

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Expert Answer

The basic formula to find the number of diagonals in a polygon is n(n-3)/2.

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Question

How many diagonals can be drawn from one vertex of nonagon?

Community Answer

You can draw six, one for each of the vertices, except for the vertex you're drawing from, and the two adjacent vertices.

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Question

What is the relationship between the number of sides in an icosikaipentagon and the number of diagonals?

Donagan

Top Answerer

It is the same relationship for any polygon, as expressed in the formula n(n-3)/2.

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Question

How would we solve it if it had (n-1) sides?

Community Answer

If you had (n-1) sides you would simply plug (n-1) into the equation as the variable: n(n - 3)/2 = (n-1)((n-1) - 3)/2. Simplifying terms yields ((n-1)(n-4))/2. You can either leave it at that, or expand using FOIL: (n^2 - 5n + 4)/2.

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Question

A pyramid has how many diagonals?

Donagan

Top Answerer

It depends on the shape of the base. A square or rectangular base has two diagonals, a pentagonal base has three diagonals, etc. The slanted surfaces are always triangles and have no diagonals.

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How do I find the measure of angle of a polygon?

Donagan

Top Answerer

If a regular polygon has n sides, each angle equals [(n-2)(180°)] / n. For example, a regular pentagon has five sides, so each interior angle is [(5 - 2)(180°)] / 5 = [(3)(180°)] / 5 = 540° / 5 = 108°. (If the polygon is not regular, there is no formula available to calculate the interior angles.)

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Question

How many diagonals can be found in a hendecagon?

Donagan

Top Answerer

Substitute 11 for (n) in either of the formulas shown above.

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Question

If a polygon has (n-1) sides, what are the number of diagonals?

Donagan

Top Answerer

Substitute (n-1) for (n) in the first formula shown above: (n-1)[(n-1) - 3] / 2 = [(n-1)(n-4)] / 2 = (n² - 5n + 4) / 2. The number of diagonals is (n² - 5n + 4) / 2.

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Question

How many diagonals has a hexadecagon?

Donagan

Top Answerer

Using the above formula, (16)(13) / 2 = 104.

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Question

In the formula,n(n-3)/2, where does -3 come from and why we need to divide it by 2?

Community Answer

The n-3 comes from picking any of the n vertices and subtracting the 3 vertices we can't draw a diagonal to, itself and the neighbouring vertices on each side. The /2 is because n(n-3) counts a diagonal from A to B, and again from B to A, even though it's really the same diagonal regardless of direction. Dividing by 2 counts corrects this overcount and counts every diagonal once.

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Question

What is the maximum possible number of diagonals in any polygon?

Community Answer

In each polygon, n(n-3)/2 is the number of maximum diagonals. If you are asking for maximum number of diagonals in a highest polygon, there are an infinite number of sides. Thus, no fixed maximum number of diagonals.

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