Write the number of diagonals of an n-sided polygon. - Vidyadip

Question

Write the number of diagonals of an n-sided polygon.

✓

Answer

Polygon has n sides and diagonals are kinds made by joining two opposite points = Number of total lines in polygon - Number of sides in the Polygon.
Number of diagonal $={^\text{n}}\text{C}_{\text{2}}-\text{n}$
$=\frac{\text{n}(\text{n}-1)}{2}-\text{n}$
$=\text{n}\Big[\frac{\text{n}-1}{2}-1\big]$
$=\text{n}\Big[\frac{\text{n}-1-2}{2}\Big]$
$=\frac{\text{n}(\text{n}-3)}{2}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the following Question.(1 Marks)" from Binomial Theorem→Binomial Theorem — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

From the sets given below, select equal sets and equivalent sets.
A = {0, a},
B = {1, 2, 3, 4},
C = {4, 8, 12},
D = {3, 1, 2, 4},
E = {1, 0},
F = {8, 4, 12},
G = {1, 5, 7, 11},
H = {a, b}.

If A and B are subsets of the universal set X and n(X) = 50, n(A) = 35, n(B) = 20, n(A’ ∩ B’) = 5, find n(A’ ∩ B)

Prove the following : $\tan ^2 \theta-\sin ^2 \theta=\sin ^4 \theta \sec ^2 \theta$

If the line $y = mx$ does not intersect the circle $(x + 10)^2 + (y + 10)^2 = 180$, then write the set of values taken by $m$.

If $X$ and $Y$ are two variates connected by the relation $\text{Y}=\frac{\text{aX+b}}{\text{c}}$ and $\text{Var}(\text{X})=\sigma^2,$ then write the expression for the standard deviation of $Y$.

Draw the angles of the following measures and determine their quadrants : – 80°

If $\frac{3+5+7+\ ...\ +\text{Upto n terms}}{5+8+11+\ ...\ \text{Upto 10 terms}}=7,$ then find the value of n.

Write the equation of the hyperbola whose vertices are $(\pm3,0)$ and foci at $(\pm5,0).$

If the lengths of semi-major and semi-minor axes of an ellipse are 2 and $\sqrt{3}$ and their corresponding equations are y - 5 = 0 and x + 3 = 0, then write the equation of the ellipse.

For the following G.P.s, find $S_n$. 3, 6, 12, 24, ……..