How many diagonals does a regular seven-sided polygon contain?
A regular seven-sided polygon is also known as a regular heptagon. I need to find the total number of diagonals that can be drawn from the vertices of the heptagon to other non-adjacent vertices. One way to approach this problem is to count how many diagonals can be drawn from each vertex and then add them up. Alternatively, I could use a formula that relates the number of sides of a polygon to the number of diagonals. I think the formula might be faster, so I'll try to recall it. I remember that for any polygon with n sides, the number of diagonals is n(n-3)/2. This makes sense, because from each vertex, I can draw n-3 diagonals to the other non-adjacent vertices, and then I have to divide by 2 to avoid counting each diagonal twice. So, plugging in n = 7, I get 7(7-3)/2 = 7(4)/2 = 14. Therefore, a regular heptagon contains 14 diagonals. 