number of diagonals in pentagon
Understand the Problem
The question is asking for the number of diagonals that can be drawn in a pentagon. To calculate the number of diagonals in any polygon, we can use the formula D = n(n - 3)/2, where n is the number of sides. In this case, since a pentagon has 5 sides, we will substitute n with 5 to find the answer.
Answer
$5$
Answer for screen readers
The number of diagonals in a pentagon is $5$.
Steps to Solve
- Identify the number of sides (n)
In this case, we have a pentagon which has 5 sides. So, we set $n = 5$.
- Substitute n into the formula
Next, we substitute $n$ into the formula for the number of diagonals, which is:
$$ D = \frac{n(n - 3)}{2} $$
Substituting $n = 5$ into the equation gives:
$$ D = \frac{5(5 - 3)}{2} $$
- Perform the calculation
Now, simplify the equation:
First calculate $(5 - 3)$:
$$ D = \frac{5 \cdot 2}{2} $$
Now, multiply $5$ and $2$:
$$ D = \frac{10}{2} $$
- Final simplification
Finally, divide $10$ by $2$:
$$ D = 5 $$
So, we find that the number of diagonals in a pentagon is 5.
The number of diagonals in a pentagon is $5$.
More Information
The formula used, $D = \frac{n(n - 3)}{2}$, is derived from combinatorial principles in geometry, specifically related to counting connections in a polygon. A pentagon is a simple shape yet allows for several unique diagonals.
Tips
- Incorrectly applying the formula: Sometimes, users confuse which formula to use for the number of diagonals or mistakenly include edges or vertices in their count.
- Forgetting to subtract: Forgetting to subtract 3 from $n$ in the formula can lead to too many diagonals being counted.
