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.
Answer for screen readers
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.
