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RD Sharma Solutions Class 8 Mathematics Solutions for Understanding Shapes Polygons Exercise 15.1 in Chapter 15 - Understanding Shapes Polygons

Question 6 Understanding Shapes Polygons Exercise 15.1

How many diagonals does each of the following have?

(i)A convex quadrilateral

(ii)A regular hexagon

(iii)A triangle

Answer:

(i)A convex quadrilateral

R D Sharma Solutions - Mathematics - Class 8 chapter Understanding Shapes Polygons Question 6 Solution image

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

R D Sharma Solutions - Mathematics - Class 8 chapter Understanding Shapes Polygons Question 6 Solution image

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

R D Sharma Solutions - Mathematics - Class 8 chapter Understanding Shapes Polygons Question 6 Solution image

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.

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