Worksheet on Symmetry and Visualising Solid Shapes

Solved Questions on Symmetry and Visualising Solid Shapes

1. What is the length of the line of symmetry AD?

a) 3.6 cm
b) 4.0 cm
c) 4.4 cm
d) 4.5 cm

Answer: b) 4.0 cm

Explanation: Both △ABD and △AB'D are similar triangles which is shown in the diagram.

In ABD,
AB2 = AD2 + BD2 [Pythagoras’ Theorem]
AD2 = AB2 − BD2
AD = AB2−BD2
AD = 52−32
AD = 25−9
AD = 16
AD = 4 × 4
AD = 4 cm

2. How many lines of symmetry are there in the given figure?

a) Two lines of symmetry
b) Three lines of symmetry
c) Four lines of symmetry
d) Infinite lines of symmetry

Answer: b) Three lines of symmetry

Explanation: There are three lines of symmetry, shown as:

3. How many cubes are present in the following structure?

a) 26
b) 36
c) 46
d) 56

Answer: c) 46

Explanation: In the structure, cubes are counted.

Number of cubes present in the given structure
= 4 + 17 + 25 = 46

4. Which of the following letter combinations best represents rotational symmetry in the word “MATHS”?

a) A and S
b) M and T
c) H and S
d) S and T

Answer: c) H and S

Explanation: Rotational symmetry is a characteristic that allows an object or word to maintain its appearance when rotated by a specific angle.
In the case of the word “MATHS”, the letters ‘H’ and ‘S’ show rotational symmetry as they remain identical when the word is rotated by 180° which is equal to a half turn. In the word “MATHS”, the pairs of letters with rotational symmetry are ‘H’ and ‘S’.

5. Which of the following is a mirror symmetry of the question figure?

a) 
b) 
c) 
d) 

Answer: c) 

Explanation: The complete figure after reflection is shown as: