Std 6 th Mathematics- 16. Quadrilaterals

Question 1:

Observe the figures below and find out their names.

              Figure              Name                                                       
(1)
                                                                         
(2)   

                                                                 

(3) 
     

(4) 



 

Answer 1:

(1) In the given figure, there are five sides.
Hence, the given figure is a Pentagon. 
(2) In the given figure, there are six sides.
Hence, the given figure is a Hexagon. 
(3) In the given figure, there are seven sides.
Hence, the given figure is a Heptagon. 
(4) In the given figure, there are eight sides.
Hence, the given figure is a Octagon.

Question 1:

Draw $\square$XYZW and name the following.
(1) The pairs of opposite angles.
(2) The pairs of opposite sides.
(3) The pairs of adjacent sides.
(4) The pairs of adjacent angles.
(5) The diagonals of the quadrilateral.
(6) The name of the quadrilateral in different ways.

Answer 1:

(1) ∠X and ∠Z, ∠Y and ∠W
(2) seg XY and seg ZW, seg XW and seg YZ
(3) seg XY and seg YZ, seg YZ and seg WZ; seg WZ and seg XW, seg XW and seg XY
(4) ∠X and ∠Y, ∠Y and ∠Z, ∠Z and ∠W, ∠X and ∠W
(5) Diagonal XZ and  Diagonal YW
(6) □YZWX, □ZWXY, □XYZW, □XWZY, □WZYX, □WXYZ etc.

Question 2:

In the table below, write the number of sides the polygon has.
 

Names	Quadrilateral	Octagon	Pentagon	Heptagon	Hexagon
Number of sides

Answer 2:

 

Names	Quadrilateral	Octagon	Pentagon	Heptagon	Hexagon
Number of sides	4	8	5	7	6

​

Question 3:

Look for examples of polygons in your surroundings. Draw them.

Answer 3:

(a) Pattern of the football is pentagonal in shape.



(b) Tablet box is heptagonal in shape


(c) Stop sign of traffic signal is in octagonal in shape
 

(d) Floor tiles are square in shape
 

Question 4:

We see polygons when we join the tips of the petals of various flowers. Draw these polygons and write down the number of sides of each polygon.

Answer 4:

(a)

Number of Sides = 4

(b)

Number of Sides = 6

(c)

Number of Sides = 14

Question 5:

Draw any polygon and divide it into triangular parts as shown here. Thus work out the sum of the measures of the angles of the polygon.

Answer 5:

As the sum of the angle of a triangle is 180∘.
Therefore, h + g + f =  180∘        ...(1)
i + e + a  =  180∘       ...(2)
b + c + d =  180∘        ...(3)
Add (1), (2) and (3)
h + g + f  + i + e + a + b + c + d = 180∘ + 180∘  + 180∘
⇒ h + i + g + f  + e + d + b + c = 540∘
⇒ E + D + C + B + A = 540∘
Therefore, the sum of the angles of a pentagon is 540∘