Chapter 15 - Understanding Shapes-I (Polygons), Class 8, Maths RD Sharma Solutions | RD Sharma Solutions for Class 8 Mathematics PDF Download

PAGE NO 15.5:

Question 1:

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

ANSWER:

(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:

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:

In polygon ABCD, AC and BD are the diagonals.

PAGE NO 15.6:

Question 4:

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

ANSWER:

(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:

(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:
An n-sided convex polygon has  diagonals.
(i) A quadrilateral has  diagonals.
There are 2 diagonals in the convex quadrilateral.


(ii) A regular hexagon has   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:

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

(i) Equilateral triangle:

(ii) Square:


(iii) Regular hexagon: