Question

How many distinct diagonals of a convex heptagon (7-sided polygon) can be drawn?

Answer 1

The convex heptagon has 14 distinct diagonals can be drawn

Step-by-step explanation:

A polygon is said to be a heptagon if it has 7 vertices, 7 sides and 7 angles. A heptagon is called a convex heptagon if the lines connecting any two non-adjacent vertices lie completely inside the heptagon

The formula of number of diagonals in any polygon is $d=\frac{n(n-3)}{2}$ , where

• d is the number of the diagonals of the polygon
• n is the number of sides of the polygon

∵ The heptagon has 7 sides

∴ n = 7

∵ The number of diagonals = $\frac{n(n-3)}{2}$

- Substitute n by 7 in the rule above

∴ The number of diagonals = $\frac{7(7-3)}{2}$

∴ The number of diagonals = $\frac{7(4)}{2}$

∴ The number of diagonals = $\frac{28}{2}$

∴ The number of diagonals = 14

The convex heptagon has 14 distinct diagonals can be drawn

Learn more:

You can learn more about the polygons in brainly.com/question/6281564

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