# 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

 Polyhedron Faces (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

 Polyhedron Faces (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

 Polyhedron Faces (F) Vertices (V) Edges (E) Does Euler՚s formula hold? (a) Illustration 4 for 3_Verify_Eulers_formula_for_the …

(a)

(a)

(b)

## (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 Shape Number of Cubes Front View Side View Top View (a) Illustration 8 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

 Solid Shape Number of Cubes Front View Side View Top View (a) Illustration 10 for 7_Choose_the_appropriate_side_ …

(a)

(a)

(a)

(b)

(c)

(d)

(a)

(a)

(a)

(a)

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

(a)

(b)

(c)

• 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.
• From Above Figure it՚s clear that given shape have 12 Face,
• From below Figure it՚s clear that given shape have 23 Edges,
• From Below Figure it՚s clear that given shape have 14 Vertices,
• Euler՚s formula stated that for any polyhedron in Face = F , Vertices = V and Edges = E then,
 Polyhedron Faces (F) Vertices (V) Edges (E) Does Euler՚s formula hold? (a) Illustration 27 for Answers_and_Explanations 12 14 23 NO

• From Above Figure it՚s clear that given shape have 8 Face,
• From below Figure it՚s clear that given shape have 12 Edges,
• 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,
 Polyhedron Faces (F) Vertices (V) Edges (E) Does Euler՚s formula hold? (b) Illustration 31 for Answers_and_Explanations 8 7 12 NO

• From Above Figure it՚s clear that given shape have 10 Face,
• From above Figure it՚s clear that given shape have 24 Edges,
• 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,
 Polyhedron Faces (F) Vertices (V) Edges (E) Does Euler՚s formula hold? (c) Illustration 35 for Answers_and_Explanations 10 16 24 YES

• 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.

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

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

• 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.
 Solid Shape Number of Cubes Front View Side View Top View (a) Illustration 41 for Answers_and_Explanations 7 i iii ii
• That means from given figure;
• figure number (i) represent Front view,
• Figure number (iii) represent Side view
• Figure number (ii) represent Top View.

• 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.
 Solid Shape Number of Cubes Front View Side View Top View (a) Illustration 44 for Answers_and_Explanations 10 iii ii i
• That means from given figure;
• figure number (i) represent Top view,
• Figure number (ii) represent Side view
• Figure number (iii) represent Front View.

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

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

• 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.

• 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.

• 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.

• 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.

• 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.
• 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

Hence for given figure Order of Symmetry is 4.

• 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
• 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

Hence for given figure Order of Symmetry is 4.

• 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.
• 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

Hence for given figure Order of Symmetry is 2.

• 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.
• 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

Hence for given figure Order of Symmetry is 2.

• 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.
• As shown in above figure; given figure is line symmetry.
• Its left-hand side part is reflection of right hand side part.

• 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