Question

How many diagonals are there in a convex n-gon?

a) n - 2
b) n - 1
c) (n * (n - 3)) / 2
d) (n * (n - 1)) / 2

Answer 1

The number of diagonals in a convex n-gon is calculated using the formula (n * (n - 3)) / 2, which accounts for all possible connections between non-adjacent vertices. The correct answer to the student's question is therefore option c.

Step-by-step explanation:

The question concerns finding the number of diagonals in a convex polygon with n sides, known as a convex n-gon. This can be calculated using a specific formula. We know that each vertex of an n-gon can be connected to n - 3 other vertices by diagonals (we subtract 3 because we cannot draw a diagonal to the vertex itself, or its two adjacent vertices). Since there are n vertices, we initially multiply n by (n - 3) to count the connections, but this counts each diagonal twice (once from each end vertex), so we must divide by 2 to adjust for this overcounting. Hence, the number of diagonals D in a convex n-gon is given by the formula D = (n * (n - 3)) / 2. Therefore, the correct answer to the question is option c, which is (n * (n - 3)) / 2.