RD Sharma Solutions (Ex 3.1): Understanding Quadrilaterals | Mathematics (Maths) Class 8 PDF Download

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RD Sharma Solutions for Class 8 Maths Chapter 15 – 
Understanding Shapes – I (Polygons) 
EXERCISE 15.1                                                    
 
1. Draw rough diagrams to illustrate the following: 
(i) Open curve 
(ii) Closed curve 
Solution: 
Here is the illustration of 
(i) Open curve  
 
 
(ii) Closed curve 
 
 
2. Classify the following curves as open or closed: 
 
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RD Sharma Solutions for Class 8 Maths Chapter 15 – 
Understanding Shapes – I (Polygons) 
EXERCISE 15.1                                                    
 
1. Draw rough diagrams to illustrate the following: 
(i) Open curve 
(ii) Closed curve 
Solution: 
Here is the illustration of 
(i) Open curve  
 
 
(ii) Closed curve 
 
 
2. Classify the following curves as open or closed: 
 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 15 – 
Understanding Shapes – I (Polygons) 
Solution: 
(i) Open curve 
(ii) Closed curve 
(iii) Closed curve 
(iv) Open curve 
(v) Open curve 
(vi) Closed curve 
 
3. Draw a polygon and shade its interior. Also draw its diagonals, if any. 
Solution: 
Here is the polygon with diagonals and with its interior shaded. 
 
 
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. 
Solution: 
(i) A closed curve that is not a polygon. 
 
(ii) An open curve made up entirely of line segments. 
 
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RD Sharma Solutions for Class 8 Maths Chapter 15 – 
Understanding Shapes – I (Polygons) 
EXERCISE 15.1                                                    
 
1. Draw rough diagrams to illustrate the following: 
(i) Open curve 
(ii) Closed curve 
Solution: 
Here is the illustration of 
(i) Open curve  
 
 
(ii) Closed curve 
 
 
2. Classify the following curves as open or closed: 
 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 15 – 
Understanding Shapes – I (Polygons) 
Solution: 
(i) Open curve 
(ii) Closed curve 
(iii) Closed curve 
(iv) Open curve 
(v) Open curve 
(vi) Closed curve 
 
3. Draw a polygon and shade its interior. Also draw its diagonals, if any. 
Solution: 
Here is the polygon with diagonals and with its interior shaded. 
 
 
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. 
Solution: 
(i) A closed curve that is not a polygon. 
 
(ii) An open curve made up entirely of line segments. 
 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 15 – 
Understanding Shapes – I (Polygons) 
(iii) A polygon with two sides. 
A polygon with two sides is not possible because, a polygon should have minimum three 
sides. 
 
5. Following are some figures: Classify each of these figures 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 
 
Solution: 
(i) It is a Simple Closed curve and a concave polygon. This is a simple closed curve and 
as a concave polygon all the vertices are not pointing outwards. 
 
(ii) It is a Simple closed curve and a convex polygon. This is a simple closed curve and as 
a convex polygon all the vertices are pointing outwards. 
 
(iii) It is Not a curve and hence it is not a polygon.  
 
(iv)  It is Not a curve and 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. 
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RD Sharma Solutions for Class 8 Maths Chapter 15 – 
Understanding Shapes – I (Polygons) 
EXERCISE 15.1                                                    
 
1. Draw rough diagrams to illustrate the following: 
(i) Open curve 
(ii) Closed curve 
Solution: 
Here is the illustration of 
(i) Open curve  
 
 
(ii) Closed curve 
 
 
2. Classify the following curves as open or closed: 
 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 15 – 
Understanding Shapes – I (Polygons) 
Solution: 
(i) Open curve 
(ii) Closed curve 
(iii) Closed curve 
(iv) Open curve 
(v) Open curve 
(vi) Closed curve 
 
3. Draw a polygon and shade its interior. Also draw its diagonals, if any. 
Solution: 
Here is the polygon with diagonals and with its interior shaded. 
 
 
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. 
Solution: 
(i) A closed curve that is not a polygon. 
 
(ii) An open curve made up entirely of line segments. 
 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 15 – 
Understanding Shapes – I (Polygons) 
(iii) A polygon with two sides. 
A polygon with two sides is not possible because, a polygon should have minimum three 
sides. 
 
5. Following are some figures: Classify each of these figures 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 
 
Solution: 
(i) It is a Simple Closed curve and a concave polygon. This is a simple closed curve and 
as a concave polygon all the vertices are not pointing outwards. 
 
(ii) It is a Simple closed curve and a convex polygon. This is a simple closed curve and as 
a convex polygon all the vertices are pointing outwards. 
 
(iii) It is Not a curve and hence it is not a polygon.  
 
(iv)  It is Not a curve and 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. 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 15 – 
Understanding Shapes – I (Polygons) 
 
(viii) It is a Simple closed curve but not a polygon. 
 
6. How many diagonals does each of the following have? 
(i) A convex quadrilateral  
(ii) A regular hexagon  
(iii) A triangle 
Solution: 
(i) A convex quadrilateral  
 
For a convex quadrilateral we shall use the formula n(n-3)/2 
So, number of diagonals = 4(4-3)/2 = 4/2 = 2 
A convex quadrilateral has 2 diagonals. 
 
(ii) A regular hexagon  
 
For a regular hexagon we shall use the formula n(n-3)/2 
So, number of diagonals = 6(6-3)/2 = 18/2 = 9 
A regular hexagon has 9 diagonals. 
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RD Sharma Solutions for Class 8 Maths Chapter 15 – 
Understanding Shapes – I (Polygons) 
EXERCISE 15.1                                                    
 
1. Draw rough diagrams to illustrate the following: 
(i) Open curve 
(ii) Closed curve 
Solution: 
Here is the illustration of 
(i) Open curve  
 
 
(ii) Closed curve 
 
 
2. Classify the following curves as open or closed: 
 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 15 – 
Understanding Shapes – I (Polygons) 
Solution: 
(i) Open curve 
(ii) Closed curve 
(iii) Closed curve 
(iv) Open curve 
(v) Open curve 
(vi) Closed curve 
 
3. Draw a polygon and shade its interior. Also draw its diagonals, if any. 
Solution: 
Here is the polygon with diagonals and with its interior shaded. 
 
 
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. 
Solution: 
(i) A closed curve that is not a polygon. 
 
(ii) An open curve made up entirely of line segments. 
 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 15 – 
Understanding Shapes – I (Polygons) 
(iii) A polygon with two sides. 
A polygon with two sides is not possible because, a polygon should have minimum three 
sides. 
 
5. Following are some figures: Classify each of these figures 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 
 
Solution: 
(i) It is a Simple Closed curve and a concave polygon. This is a simple closed curve and 
as a concave polygon all the vertices are not pointing outwards. 
 
(ii) It is a Simple closed curve and a convex polygon. This is a simple closed curve and as 
a convex polygon all the vertices are pointing outwards. 
 
(iii) It is Not a curve and hence it is not a polygon.  
 
(iv)  It is Not a curve and 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. 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 15 – 
Understanding Shapes – I (Polygons) 
 
(viii) It is a Simple closed curve but not a polygon. 
 
6. How many diagonals does each of the following have? 
(i) A convex quadrilateral  
(ii) A regular hexagon  
(iii) A triangle 
Solution: 
(i) A convex quadrilateral  
 
For a convex quadrilateral we shall use the formula n(n-3)/2 
So, number of diagonals = 4(4-3)/2 = 4/2 = 2 
A convex quadrilateral has 2 diagonals. 
 
(ii) A regular hexagon  
 
For a regular hexagon we shall use the formula n(n-3)/2 
So, number of diagonals = 6(6-3)/2 = 18/2 = 9 
A regular hexagon has 9 diagonals. 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 15 – 
Understanding Shapes – I (Polygons) 
(iii) A triangle 
 
For a triangle we shall use the formula n(n-3)/2 
So, number of diagonals = 3(3-3)/2 = 0/2 = 0 
A triangle has no diagonals. 
 
7. What is a regular polygon? State the name of a regular polygon of  
(i) 3 sides  
(ii) 4 sides  
(iii) 6 sides 
Solution: 
Regular Polygon: A regular polygon is an enclosed figure. In a regular polygon minimum 
sides are three. 
(i) 3 sides 
A regular polygon with 3 sides is known as Equilateral triangle. 
 
(ii) 4 sides 
A regular polygon with 4 sides is known as Rhombus. 
 
(iii) 6 sides 
A regular polygon with 6 sides is known as Regular hexagon.