Name: Introduction to Plane Figures
Uploaded: 2019-07-19
Duration: 6 min 17 s
Description: Plane figures are flat, two-dimensional (2D) shapes. A plane figure can be made of straight lines, curved lines, or both straight and curved lines. Watch the...

Question

Seema used the formula $\frac{n (n - 1)}{2} - n$ for finding the number of diagonals of a polygon instead of $\frac{n (n - 3)}{2}$ . Is Seema right or wrong?

Accepted Answer

We know,

A polygon of $n$ sides has $n$ vertices. By joining any two vertices of a polygon, we obtain either a side or a diagonal of the polygon.

Number of line segments obtained by joining the vertices of an $n$ sided polygon taken two at a time.

Number of diagonals $= \frac{n (n - 3) }{2} . . . (i)$ , where $n$ lines are the sides of the polygon.

The formula by which Seema calculated the number of diagonals $= \frac{n (n - 1)}{2} - n . . . (i i)$

Let us consider a rectangle.

Using equation $(i)$ , the number of diagonals of rectangle $= \frac{4 (4 - 3)}{2} = \frac{4}{2} = 2$

Using equation $(i i)$ , the number of diagonals of rectangle $= \frac{4 (4 - 1)}{2} - 4$

$= \frac{4 \times 3}{2} - 4$

$= 6 - 4 = 2$

Therefore, Number of diagonals of the rectangle using both the formulae $= 2$ .

Hence, we can conclude that Seema is right.

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S Purkayastha Mathematics Solutions for Exercise - S Purkayastha Solutions for Chapter: Understanding Quadrilaterals, Exercise 7: MENTAL MATHS

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