Number of diagonals in a pentagon
Understand the Problem
The question is asking for the formula or method to calculate the number of diagonals in a pentagon, which is a polygon with five sides. To solve this, we can use the formula for the number of diagonals in an n-sided polygon, which is given by the formula D = n(n - 3)/2, where n is the number of sides.
Answer
$5$
Answer for screen readers
The number of diagonals in a pentagon is $5$.
Steps to Solve
- Identify the number of sides
In this case, we have a pentagon, which has $n = 5$ sides.
- Apply the formula for diagonals
We will use the formula for calculating the number of diagonals in a polygon:
$$ D = \frac{n(n - 3)}{2} $$
Now we substitute $n$ with 5.
- Perform the calculations
Substituting in the values, we will calculate:
$$ D = \frac{5(5 - 3)}{2} $$
This simplifies to:
$$ D = \frac{5(2)}{2} $$
- Complete the calculation and simplify
Now simplify the expression:
$$ D = \frac{10}{2} = 5 $$
Thus, the number of diagonals in a pentagon is 5.
The number of diagonals in a pentagon is $5$.
More Information
A pentagon, being a five-sided polygon, can connect vertices with diagonals, leading to a total of 5 diagonals. This formula can be applied to any polygon as long as you know the number of its sides.
Tips
- One common mistake is forgetting to subtract 3 from the number of sides in the formula. Always remember that only the vertices that are not adjacent can contribute to diagonals.
- Another mistake is not dividing the total by 2, which accounts for the fact that each diagonal is counted twice.
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