how many triangles can you make by joining the diagonals of a pentagon?
To find out the number of triangles that can be formed by joining the diagonals of a pentagon, we need to apply a formula.
Let's start by understanding the properties of a pentagon. A regular pentagon has five sides of equal length, and each interior angle measures 108 degrees.
When we join the diagonals of a pentagon, these diagonals form smaller triangles within the pentagon. The number of triangles formed can be calculated using the formula:
Number of triangles = (n-2) * (n-1) / 2
Where 'n' represents the number of sides of the polygon.
For a pentagon, substituting n = 5 into the formula, we have:
Number of triangles = (5-2) * (5-1) / 2
= 3 * 4 / 2
= 12 / 2
= 6
Therefore, you can make 6 triangles by joining the diagonals of a pentagon.