The number of diagonals that can be drawn by joining the vertices of an octagon, is20. Options C is the right choice.
An octagon, a closed figure with eight sides, possesses a unique arrangement of vertices. Each vertex connects to three adjacent vertices to form triangles, and the remaining vertices can be linked to form diagonals, which extend beyond the existing triangles. To determine the exact number of diagonals, we can employ a mathematical formula.
Let's consider an n-sided polygon, where n represents the number of vertices.
The formula for counting the diagonals within this polygon is:
n*(n - 3) / 2
In the case of an octagon, n = 8. Substituting this value into the formula, we get:
8*(8 - 3) / 2 = 8*5 / 2 = 40 / 2 = 20
Therefore, an octagon possesses precisely 20 diagonals. This implies that we can connect 20 distinct pairs of vertices within the octagon's structure using diagonals. Options C is the right choice.
Question:-
The number of diagonals that can be drawn by joining the vertices of an octagon, is
A) 28
B) 48
C) 20
D) None of these