What polygon has 20 diagonals?I don't know how to figur this out.
THANKS!!!!
A rectangle (4 sides) has 2 diagonals.
A hexagon (6 sides) has 3 diagonals.
An octagon (8 sides) has 4 diagonals.
A _____ (20 sides) has 20 diagonals.
The no. Of diagonals in a polygon is nC2-n .So polygon with 8 sides shall have 20 diagonals
To determine the polygon with 20 diagonals, we can start by observing a pattern with the number of diagonals in polygons.
For any polygon with n sides, the formula to calculate the number of diagonals is:
Number of diagonals = n(n - 3) / 2
Now, we need to find a value of n that satisfies the equation n(n - 3) / 2 = 20.
To simplify the equation, we multiply both sides by 2 to eliminate the fraction:
2 * (n(n - 3) / 2) = 20
n(n - 3) = 40
Next, we can try different values of n until we find one that satisfies the equation. Start by substituting n = 4:
4(4 - 3) = 4
Since 4 is not equal to 40, we move on to the next value. Substituting n = 5:
5(5 - 3) = 10
Again, 10 is not equal to 40, so we continue. Substituting n = 6:
6(6 - 3) = 18
18 is not equal to 40, so we continue. Substituting n = 7:
7(7 - 3) = 28
28 is also not equal to 40. We continue with n = 8:
8(8 - 3) = 40
Finally, we found a value of n (8) that satisfies the equation. Therefore, a polygon with 20 sides is an octagon.
So, an octagon (8 sides) has 20 diagonals.