Question

Draw a rough sketch of a regular pentagon. The number of diagonals that can be drawn are
A. 3
B. 4
C. 5
D. None of the above

Answer 1

Hint: To solve this type of problem first we have to draw pentagons which have 5 sides. Now applying the formula for the number of diagonals that can be formed. The formula is
Number of diagonals \[=\dfrac{n\left( n-3 \right)}{2}\].

Complete step-by-step answer:
Step 1: Take 5 points like A, B, C, D, E.
Step 2: Join AB, BC, CD, DE, EA.
Step 3: Join AC, AD, BE, BD, CE.

Now applying the formula for number of diagonals,
Number of diagonals\[=\dfrac{n\left( n-3 \right)}{2}\] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (a)
The number of sides of a pentagon is 5.
Now substituting the value of 5 in (a).
We get,
\[=\dfrac{5\left( 5-3 \right)}{2}\]
\[=\dfrac{5\left( 2 \right)}{2}\]
\[=5\].
Therefore the number of diagonals that can be drawn is 5.
So, the correct answer is “Option C”.

Note: By applying the above formula we can find the number of diagonals for any polygon.Triangle is an exception to this rule, due to the shape of the triangle , it does not have any diagonals. Take care while drawing figures.