## RD Sharma Solutions for Class 8 Chapter 15 Understanding Shapes- I (Polygons) Free Online

EXERCISE 15.1 PAGE NO: 15.5

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

(i) Open curve

(ii) Closed curve

(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:**

**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.

(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.

**(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.

(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

(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.

**(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

(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.