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The image shows two polygons for which you are supposed to calculate the number of diagonals: a pentadecagon (15-sided polygon) and a heptagon (7-sided polygon). Let's find the number of diagonals for each.

The formula to find the number of diagonals in a polygon with \( n \) sides is given by:
\[
\text{Number of diagonals} = \frac{n(n-3)}{2}
\]

### Pentadecagon (15-sided polygon)
Plugging \( n = 15 \) into the formula gives:
\[
\text{Number of diagonals} = \frac{15(15-3)}{2} = \frac{15 \times 12}{2} = 90
\]

### Heptagon (7-sided polygon)
Plugging \( n = 7 \) into the formula gives:
\[
\text{Number of diagonals} = \frac{7(7-3)}{2} = \frac{7 \times 4}{2} = 14
\]

So, the pentadecagon has 90 diagonals and the heptagon has 14 diagonals.

Would you like more details or have any other questions?

1. How do we calculate the diagonals for a 10-sided polygon?
2. Why does the formula subtract 3 in the expression \( n(n-3) \)?
3. How many diagonals would a polygon have if it had 50 sides?
4. What is the general method to find diagonals that a vertex connects with in a polygon?
5. Can you explain why a triangle has no diagonals?

**Tip**: Diagonals of a polygon are line segments connecting any two non-adjacent vertices. This formula helps understand how complex a shape can get as the number of sides increases.

Find the total number of diagonals that can be drawn in the following polygons: Pentadecagon and Heptagon.

Learn how to calculate the number of diagonals in a pentadecagon (15-sided polygon) and a heptagon (7-sided polygon) using the formula (n(n-3))/2. This problem involves core concepts of geometry and is suitable for students in Grades 6-8.

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