RD Sharma Solutions for Class 8 Math Chapter 15 Understanding Shapes I (Polygons) are provided here with simple step-by-step explanations. These solutions for Understanding Shapes I (Polygons) are extremely popular among class 8 students for Math Understanding Shapes I (Polygons) Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the RD Sharma Book of class 8 Math Chapter 15 are provided here for you for free. You will also love the ad-free experience on Meritnationâ€™s RD Sharma Solutions. All RD Sharma Solutions for class 8 Math are prepared by experts and are 100% accurate.

#### 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.

#### Page No 15.5:

#### 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

#### Page No 15.5:

#### 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 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:

(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.

#### Page No 15.6:

#### 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.

#### Page No 15.6:

#### 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 $\frac{n(n-3)}{2}$ 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.

#### Page No 15.6:

#### 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:

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