Question

Length of the side of regular hexagon is a. What is the sum of all diagonals ?​

Answer 1

Answer:

Properties of a Regular Hexagon:

It has six sides and six angles.

Lengths of all the sides and the measurement of all the angles are equal.

The total number of diagonals in a regular hexagon is 9.

The sum of all interior angles is equal to 720 degrees, where each interior angle measures 120 degrees.

The sum of all exterior angles is equal to 360 degrees, where each exterior angle measures 60 degrees.

A diagonal is a line segment joining two non-adjacent vertices of a polygon. A regular hexagon has six sides and six vertices. One vertex has three diagonals, so a hexagon would have three diagonals times six vertices, or 18 diagonals. Divide this number by 2 to account for duplicate diagonals between two vertices. The formula for the number of vertices in a polygon is:

n⋅(n−3)2

where n=# of sides.

So,the answer is 9

Step-by-step explanation:

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Answer 2

Answer: 18

Step-by-step explanation:

• A hexagon has six sides and six angles.

• Since, it is a regular hexagon therefore the lengths of sides and the measurement of the angles will be equal.

• The total number of diagonals in a regular hexagon will be 9 according to the formulae $\frac{n(n-3)}{2}$.

• A diagonal is a line  joining two non-adjacent vertices of any polygon. As a regular hexagon has six sides and six vertices so the line joining one vertex with other three vertex makes three diagonals. Multiply this by the number of sides and then divide this result by 2 and we get the final result.
• Hence, the required number of diagonals are 18.

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