Q6 of 7 Page 16

How many diagonals does each of the following have?

(i) A convex quadrilateral


(ii) A regular hexagon


(iii) A triangle

(i) A convex quadrilateral



Convex quadrilateral has two diagonals.


(ii) A regular hexagon



An n-sided convex polygon has diagonals.


∴Applying the above relation for hexagon:


Number of diagonals =


Regular Hexagon has 9 diagonals.


(iii) A triangle



An n-sided convex polygon has diagonals.


∴Applying the above relation for triangle:


Number of diagonals =


Therefore a triangle has no diagonal


More from this chapter

All 7 →
3

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

 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.

 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

 7

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

(i) 3 sides


(ii) 4 sides


(iii) 6 sides