## RD Sharma Class 8 Solutions Chapter 15 Understanding Shapes I (Polygons) Ex 15.1

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 15 Understanding Shapes I Ex 15.1

**Question 1.**

**Draw rough diagrams to illustrate the following:**

**(i) Open curve**

**(ii) Closed curve**

**Solution:**

**Question 2.**

**Classify the following curves as open or closed.**

**Solution:**

Open curves : (i), (iv) and (v) are open curves.

(ii) , (iii), and (vi) are closed curves.

**Question 3.**

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

**Solution:**

In the given polygon, the shaded portion is its interior region AC and BD are the diagonals of polygon ABCD.

**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.**

**Solution:**

(i) Close curve but not a polygon.

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

(iii) A polygon with two sides. It is not possible. At least three sides are necessary

**Question 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.

(ii) It is a simple closed curve and convex polygon.

(iii) It is neither a curve nor polygon.

(iv) it is neither a curve 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.**

**Solution:**

(i) A convex quadrilateral

Here n = 4

**Question 7.**

**What is a regular polygon ? State the name of a regular polygon of:**

**(i) 3 sides**

**(ii) 4 sides**

**(iii) 6 sides.**

**Solution:**

A regular polygon is a polygon which has all its sides equal and so all angles are equal,

(i) 3 sides : It is an equilateral triangle.

(ii) 4 sides : It is a square.

(iii) 6 sides : It is a hexagon.

Hope given RD Sharma Class 8 Solutions Chapter 15 Understanding Shapes I Ex 15.1 are helpful to complete your math homework.

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