Answer
425.4k+ 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.
![seo images](https://www.vedantu.com/question-sets/64c94b5b-62a3-491a-a581-d86b7d8bda118915918725658422209.png)
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.
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