How Many Diagonals in a Polygon

How many diagonals are there in a polygon that has 20 sides?

• 100

• 170

• 200

• 270

How many diagonals are there in a quadrilateral?

• 1

• 2

• 3

• 4

How many diagonals have a regular hexagon?

• 9

• 5

• 7

• 8

How many diagonals does a 12-sided polygon have?

• 60

• 40

• 36

• 54

A diagonal is a line segment that joins any two non-adjacent vertices of the polygon and is not a side of the polygon. Find the number of diagonals in the given figure?

• 11

• 14

• 12

• 13

Answer explanation

The number of diagonals in heptagon are 14. Namely, AC, AD, AE, AF, BG, BF, BE, BD, CG, CF, CE, DG, DF and EG are the diagonals of given heptagon

What is the formula for the number of diagonals of a polygon with n sides?

If there is an n-sided polygon, we can calculate its number of diagonals by the formula ____

• [n(n-3)]/3

• [n(n-2)]/2

• [n(n-3)]/2

• [n(n-2)]/3

Answer explanation

Option 3 is correct as formula of diagonal of a polygon is [n(n-3)]/2

n/2n(n−3). The expression shown gives the number of diagonals in a polygon with n sides, where n is an integer. Which of the following expressions is equivalent to the expression shown?

• n²/2 −3n/2

• n²/2 +3

• n²/2 -3

Tags

CCSS.HSA.APR.D.6

How many diagonals do the pentagon have?

How many diagonals does a nonagon have?

• 27

• 18

• 21

• 28