Maths-
General
Easy

Question

A regular polygon has 20 diagonals. Find the number of sides and classify it based on the number of sides.

hintHint:

  • A regular polygon is a polygon with congruent sides and equal angles and are symmetrically placed about a common center.

The correct answer is: 8


    • We have been given in the question information about a regular polygon that has 20 diagonals which means it is an octagon.
    • We have to find the number of sides and classify it based on the number of sides.
    Step 1 of 1:
    We know that the number of diagonal in n - side polygon  equals fraction numerator n left parenthesis n minus 3 right parenthesis over denominator 2 end fraction
    Here, the number of diagonals is 20
    So,

    fraction numerator n left parenthesis n minus 3 right parenthesis over denominator 2 end fraction equals 20

    n squared minus 3 n equals 40

    n squared minus 3 n minus 40 equals 0

    (n - 8) (n + 5) = 0
    n = 8
    So, The number of sides are 8.
    And It is Octagon.

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