RD Sharma solution class 8 chapter 15 Understanding Shapes I(Polygons) Exercise 15.1

Exercise 15.1

Page-15.5

Question 1:

Draw rough diagrams to illustrate the following:
(i) Open curve
(ii) Closed curve

Answer 1:

(i) Open curve: A curve in which the beginning and the end points does not cut each other or are different.


(ii) Closed curve: A curve in which the beginning and the end points are the same and cuts each other.

Question 2:

Classify the following curves as open or closed:

Answer 2:

Open curve: A curve in which the beginning and end points are different or do not cut each other.
Closed curve: A curve in which the beginning and end points are the same and cut each other.
By the above definitions, we can classify the given figures as follows:

(i) Open curve
(ii) Closed curve
(iii) Closed curve
(iv) Open curve
(v) Open curve
(vi) Closed curve

Question 3:

Draw a polygon and shade its interior. Also draw its diagonals, if any.

Answer 3:

In polygon ABCD, AC and BD are the diagonals.

Page-15.6

Question 4:

Illustrate, if posible, each one of the following with a rough diagram:
(i) A colsed curve that is not a polygon.
(ii) An open curve made up entirely of line segments.
(iii) A polygon with two sides.

Answer 4:

(i) Polygons are made up of straight lines, not curves.


(ii) An open curve made up entirely of line segments:


(iii) Not possible because polygons are closed figures.

Question 5:

Following are some figures: Classify each of these fugures on the basis of the following:
(i) Simple curve
(ii) Simple closed curve
(iii) Polygon
(iv) Convex polygon
(v) Concave polygon
(vi) Not a curve

Answer 5:

(i) It is a simple closed curve and a concave polygon.
(ii) It is a simple closed curve and a convex polygon.
(iii) It is not a curve; hence, it is not a polygon.
(iv) It is not a curve; hence, it is not a polygon.
(v) It is a simple closed curve but not a polygon.
(vi) It is a simple closed curve but not a polygon.
(vii) It is a simple closed curve but not a polygon.
(viii) It is a simple closed curve but not a polygon.

Question 6:

How many diagonals does each of the following have?
(i) A convex quadrilateral
(ii) A regular hexagon
(iii) A triangle

Answer 6:

An n-sided convex polygon has $\frac{n(n-3)}{2}$ diagonals.
(i) A quadrilateral has $\frac{4(4-3)}{2} =2$ diagonals.
There are 2 diagonals in the convex quadrilateral.

(ii) A regular hexagon has $\frac{6(6-3)}{2}=9$ diagonals.
There are 9 diagonals in a regular hexagon.

(iii) A triangle does not have any diagonal in it.

Question 7:

What is a regular polygon? State the name of a regular polygon of
(i) 3 sides
(ii) 4 sides
(iii) 6 sides

Answer 7:

A polygon that has equal sides and equal angles is called a regular polygon.

(i) Equilateral triangle:

(ii) Square:


(iii) Regular hexagon: