How many diagonals does a regular pentagon have?

• (a) 3
• (b) 4
• (c) 5
• (d) 6

To determine how many diagonals a regular pentagon has, we can use a straightforward formula that applies to any polygon. The formula for finding the number of diagonals in a polygon is given by:

Diagonal Formula

The formula is:

D = n(n - 3) / 2

In this formula, D represents the number of diagonals, and n is the number of sides in the polygon. For a pentagon, n is 5.

Applying the Formula

Let’s plug in the value of n:

• D = 5(5 - 3) / 2
• D = 5(2) / 2
• D = 10 / 2
• D = 5

Understanding the Result

This calculation shows that a regular pentagon has 5 diagonals. To visualize this, consider a pentagon with vertices labeled A, B, C, D, and E. The diagonals can be drawn as follows:

• From A to C
• From A to D
• From B to D
• From B to E
• From C to E

Each of these lines connects non-adjacent vertices, which is the definition of a diagonal.

Visualizing with a Diagram

If you were to draw a pentagon and connect the vertices with lines, you would see that the diagonals do not include the sides of the pentagon itself. This helps reinforce the concept that a diagonal connects two vertices that are not next to each other.

Final Thoughts

So, the answer to your question is that a regular pentagon has 5 diagonals, which corresponds to option (c) in your list. Understanding how to calculate diagonals can be useful in various geometric problems and helps deepen your grasp of polygon properties.