If a polygon has 8 sides, how many diagonals does it have?

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Question: If a polygon has 8 sides, how many diagonals does it have?

Options:

Correct Answer: 20

Solution:

Using the formula n(n-3)/2, for an octagon (n=8), the number of diagonals is 8(8-3)/2 = 20.

If a polygon has 8 sides, how many diagonals does it have?

If a polygon has 8 sides, how many diagonals does it have?

Step 1: Identify the number of sides in the polygon. In this case, the polygon has 8 sides, which is called an octagon.
Step 2: Use the formula for finding the number of diagonals in a polygon, which is n(n-3)/2, where n is the number of sides.
Step 3: Substitute the number of sides (n = 8) into the formula: 8(8-3)/2.
Step 4: Calculate (8-3) which equals 5.
Step 5: Now multiply 8 by 5: 8 * 5 = 40.
Step 6: Finally, divide 40 by 2: 40 / 2 = 20.
Step 7: Therefore, the octagon has 20 diagonals.

Diagonals in Polygons – Understanding how to calculate the number of diagonals in a polygon using the formula n(n-3)/2, where n is the number of sides.