
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
487.2k+ views
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.
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.
Recently Updated Pages
Master Class 9 General Knowledge: Engaging Questions & Answers for Success

Master Class 9 English: Engaging Questions & Answers for Success

Master Class 9 Science: Engaging Questions & Answers for Success

Master Class 9 Social Science: Engaging Questions & Answers for Success

Master Class 9 Maths: Engaging Questions & Answers for Success

Class 9 Question and Answer - Your Ultimate Solutions Guide

Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

How do you graph the function fx 4x class 9 maths CBSE

Difference Between Plant Cell and Animal Cell

What is pollution? How many types of pollution? Define it

What is the color of ferrous sulphate crystals? How does this color change after heating? Name the products formed on strongly heating ferrous sulphate crystals. What type of chemical reaction occurs in this type of change.

Distinguish between Conventional and nonconventional class 9 social science CBSE
