# A polygon has 9 more diagonals than a pentagon. how many sides are in a polygon?

July 24, 2021 | education

| To calculate the number of diagonals of a convex polygon, we use the formula: N = n * (n – 3) / 2, where n is the number of vertices of the convex polygon.

Let’s calculate how many diagonals a geometric figure has – a pentagon:

5 * (5 – 3) / 2 = 5.

Let’s calculate how many diagonals a figure has if we know that it has nine more diagonals:

5 + 9 = 14.

Let’s find out what kind of figure it is:

n ^ 2 – 3n – 28 = 0;

D = 9 + 4 * 28 = 121;

n1 = (3 + 11) / 2 = 7;

n2 = (3-11) / 2 = -4;

Answer: Heptagon.

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