What is the number of diagonals in a

Question:

What is the number of diagonals in a

(i) heptagon

(ii) octagon

(iii) polygon of 12 sides?

Solution:

Number of diagonal in an $\mathrm{n}$-sided polygon $=\frac{n(n-3)}{2}$

(i) For a heptagon:

$n=7 \Rightarrow \frac{n(n-3)}{2}=\frac{7(7-3)}{2}=\frac{28}{2}=14$

(ii) For an octagon:

$n=8 \Rightarrow \frac{n(n-3)}{2}=\frac{8(8-3)}{2}=\frac{40}{2}=20$

(iii) For a 12-sided polygon:

$n=12 \Rightarrow \frac{n(n-3)}{2}=\frac{12(12-3)}{2}=\frac{108}{2}=54$

Leave a comment

Close
faculty

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now