How many diagonals are in a hexagon?

Understand the Problem

The question is asking for the number of diagonals in a hexagon. To find the number of diagonals in a polygon, we can use the formula: diagonal = n(n - 3)/2, where n is the number of sides of the polygon. In this case, n is 6 for a hexagon.

Answer

The number of diagonals in a hexagon is 9.

Steps to Solve

Identify the number of sides in a hexagon

A hexagon has 6 sides. Here, we let $n = 6$.

Use the diagonal formula

We will apply the formula for diagonals, which is $$ \text{diagonals} = \frac{n(n - 3)}{2} $$

Plug in the number of sides

Substituting $n = 6$ into the formula gives us:

$$ \text{diagonals} = \frac{6(6 - 3)}{2} $$

Simplify the expression

Calculate the expression step by step:

First, simplify $(6 - 3)$:

$$ 6 - 3 = 3 $$

Then, multiply:

$$ 6 \times 3 = 18 $$

Now divide by 2:

$$ \text{diagonals} = \frac{18}{2} = 9 $$

The number of diagonals in a hexagon is 9.

More Information

A hexagon is a polygon with six sides, and it can form a variety of triangles and quadrilaterals when connecting its vertices with diagonals. Each diagonal connects two non-adjacent vertices.

Tips

Failing to subtract 3 from the number of sides ($n - 3$), leading to incorrect diagonal calculations.
Forgetting to divide the product by 2, which gives the wrong total number of diagonals.

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