Ex.3.1 Q2 Understanding Quadrilaterals Solution - NCERT Maths Class 8

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Question

How many diagonals does each of the following have?

(a) A convex quadrilateral

(b) A regular hexagon

(c) A triangle 

Text Solution

What is known? 

Polygons with known number of vertices.

What is unknown? 

Number of diagonals

Reasoning:

A diagonal is a line segment connecting two non-consecutive vertices of a polygon. Draw the above given polygon and mark vertices and then, draw lines joining the two non-consecutive vertices. From this, we can calculate the number of diagonals.

(a) Convex quadrilateral

A convex quadrilateral has two diagonals.

Here, \(AC\) and \(BD\) are two diagonals.  

(b) A regular hexagon

Here, the diagonals are \(AD, \,AE,\, BD,\, BE,\, FC,\, FB, \,AC,\, EC\) and \(FD.\) Totally there are \(9\) diagonals.

(c) A triangle

A triangle has no diagonal because there no two non-consecutive vertices.

  
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