🎧 New: AI-Generated Podcasts Turn your study notes into engaging audio conversations. Learn more

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

  1. Identify the number of sides Since we are dealing with a hexagon, we identify that the number of sides, $n$, is 6.

  2. 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: $$ D = \frac{6(6-3)}{2} $$

  3. Calculate the expression First, calculate the value within the parentheses: $$ D = \frac{6 \times 3}{2} $$

Then perform the multiplication: $$ D = \frac{18}{2} $$

  1. 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.
Thank you for voting!
Use Quizgecko on...
Browser
Browser