**Chapter 5 Understanding Elementary Shapes Ex. 5.8**

Question 1.

Examine whether the following are polygons. If any one among them is not, say why?

Solution:

(a) The given figure is not closed. Therefore, it is not a polygon.

(b) The given figure is a polygon.

(c) The given figure is not a polygon because every polygon is enclosed with line segments.

(d) The given figure is not a polygon because it is enclosed by an arc and two line segments.

Question 2.

Name the polygon.

Make two more examples of each of these.

Solution:

(a) A quadrilateral Examples:

(b) A Triangle

Examples:

(c) A Pantagon

Examples:

(d) A Octagon

Examples:

Question 3.

Draw a rough sketch of a regular hexagon. Connecting any three of its vertices, draw a triangle. Identify the type of the triangle you have drawn.

Solution:

ABCDEF is a rough sketch of a regular hexagon. If we join any three vertices like D, A and B, we get a scalene triangle DAB.

But if we join the alternate vertices, we get an equilateral triangle EAC.

Question 4.

Draw a rough sketch of a regular octagon. (Using squared paper if you wish). Draw a rectangle by joining exactly four of the vertices of the octagon.

Solution:

ABCDEFGH is a rough sketch of regular octagon. GHCD is the rectangle formed by joining the four vertices of the given octagon.

Question 5.

A diagonal is a line segment that joins any two vertices of the polygon and is not a side of the polygon. Draw a rough sketch of a pentagon and draw its diagonals.

Solution:

A B C D E is the rough sketch of a pentagon.

By joining its any two vertices, we get, the following diagonals.