how many triangles can you make by joining the diagonals of a pentagon?
To find out how many triangles you can make by joining the diagonals of a pentagon, we can use a formula.
The formula to calculate the number of triangles formed by joining the diagonals of an n-sided polygon (in this case, a pentagon with five sides) is given by:
Number of triangles = (n−2) × (n−4) / 2
So for a pentagon, we substitute n = 5 into the formula:
Number of triangles = (5−2) × (5−4) / 2
= 3 × 1 / 2
= 3 / 2
= 1.5
Since the number of triangles must be a whole number, this tells us that you can make 1 triangle by joining the diagonals of a pentagon.