What is the formula of diagonal of polygon?

The number of diagonals of a polygon = n(n−3)/2 ‘n’ is the number of sides polygon has.

How many diagonals are in a convex polygon?

For a convex n-sided polygon, there are n vertices, and from each vertex you can draw n-3 diagonals, so the total number of diagonals that can be drawn is n(n-3).

What is convex polygon diagonals?

Given n > 3, find number of diagonals in n sided convex polygon. According to Wikipedia, In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge. Informally, any sloping line is called diagonal. Examples : Input : 5 Output : 5.

What is the formula for a convex polygon?

Theorem 39: If a convex polygon has n sides, then its interior angle sum is given by the following equation: S = ( n −2) × 180°.

How many diagonals has a convex 7 polygon?

How does a heptagon have 14 diagonals? Heptagon is a polygon ( a closed shape made up of line segments) made up of 7 sides and 7 angles. … There are 14 diagonals in a heptagon and in the given heptagon the blue line segments represent the diagonals.

How many diagonals does a convex polygon with N vertices have?

Therefore, Number of diagonals of the polygon = 2n(n−1)−n=2n(n−3).

How many diagonals are there in convex pentagon?

For n = 5, we have a pentagon with 5 diagonals. Therefore, the number of diagonals in a polygon pentagon is 5. For n = 6, n-polygon is called hexagon and it has 9 diagonals.

What is convex polygon theorem?

The exterior angle sum theorem states that the sum of the exterior angles of a convex polygon is 360°. If a convex polygon is regular with “n” number of sides, then each exterior angle of a convex polygon is measured as 360°/n.

How many diagonals does a convex triangle have?

0
Summary: (a) The number of diagonals a convex quadrilateral has is 2. (b) The number of diagonals a regular hexagon has is 9. (c) The number of diagonals a triangle has is 0.

How many diagonals can you draw INA convex heptagon a 7b 9c 14d 28?

Given: Heptagon has 7 sides. ∴ Diagonals in a heptagon are 14.

How many diagonals are in a 8 sided polygon?

20 diagonals
There are 20 diagonals in a regular octagon.