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 any polygon, you can use the formula \( D = rac{n(n-3)}{2} \), where \( n \: \) is the number of sides of the polygon. In this case, a hexagon has 6 sides.
Answer
$9$
Answer for screen readers
The number of diagonals in a hexagon is $9$.
Steps to Solve
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Identify the number of sides Since we are dealing with a hexagon, we identify that the number of sides, $n$, is 6.
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Apply the formula for diagonals We will use the formula for the number of diagonals in a polygon: $$ D = \frac{n(n-3)}{2} $$ Replacing $n$ with 6, we calculate: $$ D = \frac{6(6-3)}{2} $$
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Calculate the expression First, calculate the value within the parentheses: $$ D = \frac{6 \times 3}{2} $$
Then perform the multiplication: $$ D = \frac{18}{2} $$
- Final division to find the number of diagonals Now, divide to find the result: $$ D = 9 $$
The number of diagonals in a hexagon is $9$.
More Information
In geometry, a hexagon is a polygon with six sides. The number of diagonals can be understood as line segments that connect non-adjacent vertices. The formula applies to any polygon, making it a versatile tool in geometry.
Tips
- Forgetting to subtract 3 from $n$. It's important to ensure that you correctly follow the formula to avoid miscalculating.
- Confusing the formula for the number of sides with the formula for diagonals. Always double check which formula is being used.
