Grade 7 Shape and Symmetry Worksheet (For CBSE, ICSE, IAS, NET, NRA 2022)

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(1) Verify Euler՚s Formula for the Given Polyhedrons

Table Supporting: 1_Verify_Eulers_formula_for_the_given_polyhedrons
PolyhedronFaces (F)Vertices (V)Edges (E)Does Euler՚s formula hold?
(a)
Illustration 2 for 1_Verify_Eulers_formula_for_the …

(2) Verify Euler՚s Formula for the Given Polyhedrons

Table Supporting: 2_Verify_Eulers_formula_for_the_given_polyhedrons
PolyhedronFaces (F)Vertices (V)Edges (E)Does Euler՚s formula hold?
(a)
Illustration 3 for 2_Verify_Eulers_formula_for_the …

(3) Verify Euler՚s Formula for the Given Polyhedrons

Table Supporting: 3_Verify_Eulers_formula_for_the_given_polyhedrons
PolyhedronFaces (F)Vertices (V)Edges (E)Does Euler՚s formula hold?
(a)
Illustration 4 for 3_Verify_Eulers_formula_for_the …

(4) Draw a Net for the Given Solid Shape

(a)

Illustration 5 for 4_Draw_a_net_for_the_given_solid_shape

(5) Name of the Polyhedron That Can be Formed Using Each Net

(a)

Illustration 6 for 5_Name_of_the_polyhedron_that_c …

(b)

Illustration 7 for 5_Name_of_the_polyhedron_that_c …

(6) Choose the Appropriate Side View, Front View and Top View for Each of the Solid Shapes from the Given Views. Also, Write in the Number of Cubes Used in Each Solid Shape

Table Supporting: 6_Choose_the_appropriate_side_view_front_view_and_top_view_for_each_of_the_solid_shapes_from_the_given_views_Also_write_in_the_number_of_cubes_used_in_each_solid_shape
Solid ShapeNumber of CubesFront ViewSide ViewTop View
(a)
Illustration 8 for 6_Choose_the_appropriate_side_v …
Illustration 9 for 6_Choose_the_appropriate_side_v …

(7) Choose the Appropriate Side View, Front View and Top View for Each of the Solid Shapes from the Given Views. Also, Write in the Number of Cubes Used in Each Solid Shape

Table Supporting: 7_Choose_the_appropriate_side_view_front_view_and_top_view_for_each_of_the_solid_shapes_from_the_given_views_Also_write_in_the_number_of_cubes_used_in_each_solid_shape
Solid ShapeNumber of CubesFront ViewSide ViewTop View
(a)
Illustration 10 for 7_Choose_the_appropriate_side_ …
Illustration 11 for 7_Choose_the_appropriate_side_ …

(8) Draw the Front View, Top View, and Side View of the Given Solid Shapes

(a)

Illustration 12 for 8_Draw_the_front_view_top_view …

(9) Draw the Front View, Top View, and Side View of the Given Solid Shapes

(a)

Illustration 13 for 9_Draw_the_front_view_top_view …

(10) Write Out the Name of These Shape of the Vertical/Horizontal Cross-Section

(a)

Math. 7. G. 3 7. G. A. 3

(b)

Illustration 14 for 10_Write_out_the_name_of_these …

(c)

Illustration 15 for 10_Write_out_the_name_of_these …

(d)

Illustration 16 for 10_Write_out_the_name_of_these …

(11) Tick (√) if the Given Figure Has Rotational Symmetry. Also Write in the Order of Symmetry of Each Figure

(a)

Illustration 17 for 11_Tick________if_the_given_figure_h …

(12) Tick (√) if the Given Figure Has Rotational Symmetry. Also Write in the Order of Symmetry of Each Figure

(a)

Illustration 18 for 12_Tick________if_the_given_figure_h …

(13) Tick (√) if the Given Figure Has Rotational Symmetry. Also Write in the Order of Symmetry of Each Figure

(a)

Illustration 19 for 13_Tick________if_the_given_figure_h …

(14) Tick (√) if the Given Figure Has Rotational Symmetry. Also Write in the Order of Symmetry of Each Figure

(a)

Illustration 20 for 14_Tick________if_the_given_figure_h …

(15) Write That Given Figure Has Rotational Symmetry or Line Symmetry

(a)

Illustration 21 for 15_Write_that_Given_figure_has …

(b)

Illustration 22 for 15_Write_that_Given_figure_has …

(c)

Illustration 23 for 15_Write_that_Given_figure_has …

Answers and Explanations

Answer 1 (A)

  • Faces (F) :- Flat surface enclosed by the edges are called faces, for solid it՚s a two dimensional.
  • Edge (E) :- The line segment that from the skeleton of the solid shape are called edges.
  • Vertices (V) :- The corner where the edges meet are called vertices.
    Illustration 24 for Answers_and_Explanations
  • From Above Figure it՚s clear that given shape have 12 Face,
  • From below Figure it՚s clear that given shape have 23 Edges,
Illustration 25 for Answers_and_Explanations
  • From Below Figure it՚s clear that given shape have 14 Vertices,
    Illustration 26 for Answers_and_Explanations
  • Euler՚s formula stated that for any polyhedron in Face = F , Vertices = V and Edges = E then,
Table Supporting: Answers_and_Explanations
PolyhedronFaces (F)Vertices (V)Edges (E)Does Euler՚s formula hold?
(a)
Illustration 27 for Answers_and_Explanations
121423

NO

Answer 2 (A)

Illustration 28 for Answers_and_Explanations
  • From Above Figure it՚s clear that given shape have 8 Face,
    Illustration 29 for Answers_and_Explanations
  • From below Figure it՚s clear that given shape have 12 Edges,
    Illustration 30 for Answers_and_Explanations
  • From Below Figure it՚s clear that given shape have 7 Vertices,
  • Euler՚s formula stated that for any polyhedron in Face = F , Vertices = V and Edges = E then,
Table Supporting: Answers_and_Explanations
PolyhedronFaces (F)Vertices (V)Edges (E)Does Euler՚s formula hold?
(b)
Illustration 31 for Answers_and_Explanations
8712

NO

Answer 3 (A)

Illustration 32 for Answers_and_Explanations
  • From Above Figure it՚s clear that given shape have 10 Face,
    Illustration 33 for Answers_and_Explanations
  • From above Figure it՚s clear that given shape have 24 Edges,
    Illustration 34 for Answers_and_Explanations
  • From above Figure it՚s clear that given shape have 16 Vertices,
  • Euler՚s formula stated that for any polyhedron in Face = F , Vertices = V and Edges = E then,
Table Supporting: Answers_and_Explanations
PolyhedronFaces (F)Vertices (V)Edges (E)Does Euler՚s formula hold?
(c)
Illustration 35 for Answers_and_Explanations
101624

YES

Answer 4 (A)

  • Net is simply a sheet of cardboard whose folding gives the polyhedron.
  • Means net is a figure, can be drawn on paper and if we cut this figure (paper) along edges and bend paper along edges than it will become a polyhedron.
  • Net of given polyhedron is given below.
Illustration 36 for Answers_and_Explanations

Answer 5 (A)

  • Polyhedron that can be formed using given net is given below.
  • And name of this polyhedron is:- “Prism”
Illustration 37 for Answers_and_Explanations

Answer 5 (B)

  • Polyhedron that can be formed using given net is given below.
  • And name of this polyhedron is:- “Cuboid”
Illustration 38 for Answers_and_Explanations

Answer 6 (A)

Illustration 39 for Answers_and_Explanations
  • From Given figure it՚s clear that solid shape have 7number of cubes
  • And for the side view, top view and front view of given figure number, below table shows the figure number that represent side view, top view and front view.
Illustration 40 for Answers_and_Explanations
Table Supporting: Answers_and_Explanations
Solid ShapeNumber of CubesFront ViewSide ViewTop View
(a)
Illustration 41 for Answers_and_Explanations
7iiiiii
  • That means from given figure;
  • figure number (i) represent Front view,
  • Figure number (iii) represent Side view
  • Figure number (ii) represent Top View.

Answer 7 (A)

Illustration 42 for Answers_and_Explanations
  • From Given figure it՚s clear that solid shape have 10 number of cubes
  • And for the side view, top view and front view of given figure number, below table shows the figure number that represent side view, top view and front view.
Illustration 43 for Answers_and_Explanations
Table Supporting: Answers_and_Explanations
Solid ShapeNumber of CubesFront ViewSide ViewTop View
(a)
Illustration 44 for Answers_and_Explanations
10iiiiii
  • That means from given figure;
  • figure number (i) represent Top view,
  • Figure number (ii) represent Side view
  • Figure number (iii) represent Front View.

Answer 8 (A)

Front view, Top view and side view of given figure is given below.

Illustration 45 for Answers_and_Explanations
Illustration 46 for Answers_and_Explanations
Illustration 47 for Answers_and_Explanations

Answer 9 (A)

Front view, Top view and side view of given figure is given below.

Illustration 48 for Answers_and_Explanations
Illustration 49 for Answers_and_Explanations
Illustration 50 for Answers_and_Explanations

Answer 10 (A)

  • Horizontal cross section obtained when the plane pass through the solid object is parallel to its base.
  • And Vertical Cross section obtained when the plane pass through the solid object is vertical to its base.
  • In given figure plane pass through the parallel to base of figure.
  • So it՚s a horizontal cross section.

Answer 10 (B)

  • Horizontal cross section obtained when the plane pass through the solid object is parallel to its base.
  • And Vertical Cross section obtained when the plane pass through the solid object is vertical to its base.
  • In given figure plane pass through the vertical to base of figure.
  • So it՚s a vertical cross section.

Answer 10 (C)

  • Horizontal cross section obtained when the plane pass through the solid object is parallel to its base.
  • And Vertical Cross section obtained when the plane pass through the solid object is vertical to its base.
  • In given figure plane pass through the parallel to base of figure.
  • So it՚s a horizontal cross section.

Answer 10 (D)

  • Horizontal cross section obtained when the plane pass through the solid object is parallel to its base.
  • And Vertical Cross section obtained when the plane pass through the solid object is vertical to its base.
  • In given figure plane pass through the parallel to base of figure.
  • So it՚s a horizontal cross section.

Answer 11 (A)

  • The given figure is said to be a rotational symmetry if we get the same figure as original even after some degree rotation of figure on its own axis.
  • From below figure its clear that we will get the same figure as original even after we rotate given figure to 90 degree clock wise.
  • So given figure has a rotational symmetry.
    Illustration 51 for Answers_and_Explanations
  • Order of Symmetry: means if we rotate the figure from zero degree to 360 degree than in between how many times we get the same figure as original
  • This can be find out by divide the total rotational angle by angle of symmetry.
  • Angle of symmetry is an angle at which if we rotate the given figure than we may have same as original figure.
  • Now for given figure as shown below Angle of Symmetry
Illustration 52 for Answers_and_Explanations

Hence for given figure Order of Symmetry is 4.

Answer 12 (A)

  • The given figure is said to be a rotational symmetry if we get the same figure as original even after some degree rotation of figure on its own axis.
  • From below figure it՚s clear that we will get the same figure as original even after we rotate given figure to 90 degree clock wise.
  • So given figure has a rotational symmetry
    Illustration 53 for Answers_and_Explanations
  • Order of Symmetry: means if we rotate the figure from zero degree to 360 degree than in between how many times we get the same figure as original
  • This can be find out by divide the total rotational angle by angle of symmetry.
  • Angle of symmetry is an angle at which if we rotate the given figure than we may have same as original figure.
  • Now for given figure as shown below Angle of Symmetry
Illustration 54 for Answers_and_Explanations

Hence for given figure Order of Symmetry is 4.

Answer 13 (A)

  • The given figure is said to be a rotational symmetry if we get the same figure as original even after some degree rotation of figure on its own axis.
  • From below figure it՚s clear that we will get the same figure as original even after we rotate given figure to 180 degree clock wise.
  • So given figure has a rotational symmetry.
    Illustration 55 for Answers_and_Explanations
  • Order of Symmetry: means if we rotate the figure from zero degree to 360 degree than in between how many times we get the same figure as original
  • This can be find out by divide the total rotational angle by angle of symmetry.
  • Angle of symmetry is an angle at which if we rotate the given figure than we may have same as original figure.
  • Now for given figure as shown below Angle of Symmetry
Illustration 56 for Answers_and_Explanations

Hence for given figure Order of Symmetry is 2.

Answer 14 (A)

  • The given figure is said to be a rotational symmetry if we get the same figure as original even after some degree rotation of figure on its own axis.
  • From below figure it՚s clear that we will get the same figure as original even after we rotate given figure to 180 degree clock wise.
  • So given figure has a rotational symmetry.
    Illustration 57 for Answers_and_Explanations
  • Order of Symmetry: means if we rotate the figure from zero degree to 360 degree than in between how many times we get the same figure as original
  • This can be find out by divide the total rotational angle by angle of symmetry.
  • Angle of symmetry is an angle at which if we rotate the given figure than we may have same as original figure.
  • Now for given figure as shown below Angle of Symmetry
Illustration 58 for Answers_and_Explanations

Hence for given figure Order of Symmetry is 2.

Answer 15 (A)

  • The given figure is said to be a rotational symmetry if we get the same figure as original even after some degree rotation of figure on its own axis.
  • The given figure is said to be a line symmetry if one half of figure is reflection of other half.
    Illustration 59 for Answers_and_Explanations
  • As shown in above figure; given figure is line symmetry.
  • Its left-hand side part is reflection of right hand side part.

Answer 15 (B)

  • The given figure is said to be a rotational symmetry if we get the same figure as original even after some degree rotation of figure on its own axis.
  • The given figure is said to be a line symmetry if one half of figure is reflection of another half
    Illustration 60 for Answers_and_Explanations
  • As shown in figure. The given figure has line symmetry as well rotary symmetry.

Answer 15 (C)

  • The given figure is said to be a rotational symmetry if we get the same figure as original even after some degree rotation of figure on its own axis.
  • The given figure is said to be a line symmetry if one half of figure is reflection of another half.
    Illustration 61 for Answers_and_Explanations
  • As shown in above figure; given figure is line symmetry.
  • Its left-hand side part is reflection of right-hand side part.

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