Practicing with Maths Mela Class 5 Solutions Chapter 7 Shapes and Patterns Question Answer NCERT Solutions improves a student’s confidence in the subject.
Class 5 Maths Chapter 7 Shapes and Patterns Question Answer Solutions
Shapes and Patterns Class 5 Maths Solutions
Class 5 Maths Chapter 7 Solutions
Weaving Mats (NCERT Pg 92-93)
Question 1.
Let us make paper mats.
You will need-A coloured paper (30 cm long and 20 cm wide) and eight paper strips of two different colours (3 cm wide and longer than 20 cm).
(a) Take a coloured paper 30 cm long and 20 cm wide.
(b) Fold the coloured paper in half along the longer side.
(c) Draw vertical lines at equal distances from the closed end and cut slits leaving a gap of 3 cm at the top.
(d) Carefully unfold the paper. There will be no cuts in the paper at the top and the bottom.
(e) Now cut 8 paper strips of 3 cm width in 2 colours and of length slightly longer than 20 cm .
(f) Take one colour strip and weave it across the slits going 1 under and 1 over and again 1 under and 1 over. Repeat it for the first row.
(g) Take one more strip of another colour and weave it across the slits going 1 over and 1 under and again 1 over and 1 under. Repeat it for the second row.
(h) Weave all the strips in the same alternating pattern. Neatly fold any extra strip ends behind the mat. Your mat is ready!
Answer:
Do yourself.
Question 2.
Can you work out the steps for any of these designs and weave the pattern?
Write the steps of the pattern in your notebook for each row until it starts repeating.
Answer:
For design (i),
Row 1-1 under, 3 over, 3 under, 3 over (repeat)
Row 2-3 over, 3 under, 3 over, 3 under (repeat)
Row 3-2 over, 3 under, 3 over, 3 under (repeat)
Row 4-2 under, 3 over, 3 under, 3 over (repeat)
Row 5-3 under, 3 over, 3 under, 3 over (repeat)
Row 6-1 over, 3 under, 3 over, 3 under (repeat)
Continue weaving in this order.
For design (ii),
Row 1-1 under, 3 over, 1 under, 3 over, 1 under (repeat)
Row 2-2 under, 1 over, 3 under, 1 over, 3 over (repeat)
Row 3-1 over, 3 under, 1 over, 3 under (repeat)
Row 4-2 over, 1 under, 3 over, 1 under, (repeat)
Continue weaving in this order.
Let Us Try (NCERT Pg 93)
Question 3.
Draw the following pattern on a grid paper.
Part of it is done for you. Now, complete the rest of the grid to get the full design.
Answer:
Do yourself.
Find Out (NCERT Pg 94-97)
Question 4.
(i) Can regular triangles fit together at a point without any gap? How many of them fit together? (A sample triangle is given at the end of the book).
Do you see that regular triangles fit around a point as shown here?
(ii) Can squares (a regular 4 -sided shape) fit together around a point without any gap or overlap? Try it out using cutouts of squares (a sample square is given at the end of the book). How many squares did you need?
(iii) Can five squares fit together around a point without any gaps or overlaps? Why or why not?
(iv) Can regular hexagons ( 6 -sided shapes with equal sides) fit together around a point without any gaps or overlaps? Try. and see (a sample hexagon is given at the end of the book). How many fit together at a point?
Answer:
(i) Yes, regular triangles (equilateral triangles) fit together at a point without any gaps or overlaps.
Also, we can see that regular triangles fit around a point.
(ii) Yes, squares fit together around a point without any gaps or overlaps. Four squares are needed.
(iii) No, five squares cannot fit together around a point without any gaps or overlaps.
(iv) Yes, regular hexagons can fit together around a point without any gaps or overlaps.
We should need three regular hexagons to fit together at a point.
Question 5.
Here is a tessellating pattern with more than one shape. What shapes have been used in this pattern? ……….
……….
Answer:
The tessellation pattern in the image is composed of two shapes :
(i) Hexagons These are the larger, light-brown shapes that form the repeating main structure of the pattern.
(ii) Triangles These are the smaller, light-blue shapes that fill the gaps between the hexagons. They are specifically equilateral triangles, as seen in their arrangement at the vertices of the hexagons.
Question 6.
Continue the pattern given below and colour it appropriately.
Answer:
Do yourself.
Question 7.
(i) Look at the pattern given below. What shapes are coming together at the marked points? Are the same set of shapes coming together at these points?
(ii) Continue the pattern and colour it appropriately.
Answer:
(i) In the given figure, at the marked points (indicated by red dots), four octagons (green) and our square (blue) are coming together. The squares are formed by the corners of the octagons.
Yes, the same set of shapes (four octagons and our square) are coming together at these marked points, forming a repeating unit within the larger pattern.
(ii) Do yourself.
Question 8.
(i) Here is a tiling pattern made using two different shape-squares and triangles. Are the triangles equilateral? Why or why not?
(ii) What shapes are coming together at the marked points?
(iii) Are the same set of shapes coming together at these points?
(iv) Continue the pattern and colour it appropriately.
(v) Create similar patterns using other cutouts of shapes.
Answer:
(i) No, the triangles are not equilateral. An equilateral triangle has all sides of equal length. In the tiling pattern shown, the triangles are formed by two equal sides (sides of square). So, the triangle will be isosceles.
(ii) At the marked points in the tiling pattern, squares and triangles are coming together.
(iii) Yes, the same set of shapes (square and triangles) are coming together at these points, forming a repeating pattern where the vertices of these shapes meet at a common point.
(iv) Do yourself.
(v) Do yourself.
Question 9.
(i) You will find a copy of this rhombus at the end of the book. Cut out the triangular pieces for the following activities.
(ii) What geometrical shapes can you make by fitting 2 of these triangles together? Trace the shapes you created.
(a) How many different types of triangles can you make?
(b) Now, observe and measure the sides of these triangles. What do you notice?
(iii) Trace the isosceles triangles on a paper and cut them out. Fold them in half. What do you notice about their angles?
Answer:
(i) Do yourself.
(ii) Do yourself.
(iii) Do yourself.
Question 10.
Is it possible to make a triangle where all three sides are equal (equilateral triangle)?
Answer:
Yes, it is possible to make a triangle where all three sides are equal. This type of triangle is called an equilateral triangle. In an equilateral triangle, all three sides are of equal length and all three internal angles are also equal.
Question 11.
Is it possible to make a triangle where all three sides are unequal?
Answer:
Yes, it is possible to make a triangle where all three sides are unequal.
This type of triangle is called a scalene triangle. In a scalene triangle, all three sides have different lengths and all three angles also have different measures.
Try This (NCERT Pg 97-99)
Question 12.
(i) Cut the equilateral triangle provided at the end of the book.
(ii) Check if all the angles of an equilateral triangle are equal-just like you did with the Isosceles triangle.
(iii) Cut the equilateral triangle in half.
(iv) How many sides of each new triangle are equal?
Check in scalene triangles whether any two or more angles are equal?
Answer:
(i) Do yourself.
(ii) Yes, all angles of an equilateral triangle are equal.
(iii) Do yourself.
(iv) When a equilateral triangle is cut in half, it forms two right-angled triangles. Each of these new triangles will have three equal corresponding sides to each other.
(v) No, in a scalene triangle, all three sides and three angles are different measures.
Question 13.
How many different 4-sided shapes (quadrilaterals) can you make?
Answer:
There are infinitely different 4 -sided shapes (quadrilaterals) that can be made.
This is because the lengths of sides and angles of a quadrilateral can be varied continuously, leading to an endless number of possible combinations.
While these are specific classifications of quadrilaterals like squares, rectangles, parallelograms, kites etc.
Question 14.
(i) Measure the sides of each of these two quadrilaterals A and B. What do you notice?
(ii) Are there any pairs of sides that are equal? Which pairs are equal-adjacent or opposite?
Answer:
(i) For quadrilateral A, using a ruler, measure the lengths of all four sides. We will observe that the opposite sides are equal in length. For quadrilateral B, using a ruler, measure the lengths of all four sides.
We will observe that the opposite sides are équal in length.
(ii) In both quadrilateral A and B, the opposite sides are equal in length because the top side is equal to the bottom side and the left side is equal to right side.
Question 15.
What types of angles do quadrilaterals A and B have? Which angles are equal in each of the above parallelograms?
Answer:
In quadrilateral A,
angles Q and S are acute angles and angles P and R are obtuse angles.
Here, two pairs of opposite angles are equal. In quadrilateral B, all angles are equal and are right angles.
Question 16.
In the grid given below, draw two different kites and parallelograms each.
Answer:
Do yourself.
Question 17.
(i) Now, use 3 triangles from the rhombus to form shapes. How many sides do each one of them have?
(ii) Using 3 triangular pieces of the rhombus, try creating a (a) 3 -sided shape, (b) 4-sided shape and (c) 5 -sided shape.
Answer:
(i) Each of them has 3 sides.
(ii) (a) No, we cannot make a perfect 3 -sided shape using 3 triangles because a triangle has only 3 sides, when we combine 3 triangular pieces, the result will have more than 3 sides unless they overlap.
(b) Combining three triangular pieces can form various quadrilaterals.
(c) Combining three triangular pieces can form various pentagons.
Question 18.
Which of these shapes can be made with all 4 pieces? Try and find out.
(a) Square
(b) Rectangle
(c) Triangle
(d) Pentagon (5-sided)
(e) Hexagon (6-sided)
(f) Octagon (8-sided)
Answer:
Square and rectangle can be made with all 4 triangular pieces.
Tangram (NCERT Pg 99)
Question 19.
(i) Look at the tangram set given at the end of your textbook. Cut out all the shapes. Name them.
(a) How are they same or different from each other?
(b) What do you notice about the angles of each of the shapes?
(c) What do you notice about the sides of each of the shapes?
(ii) Now, use some or all of the pieces of your tangram set to make the following shapes. There may be more than one way to do it.
Answer:
(i) The standard tangram set consists of seven pieces which has two large right angled triangles, one medium right angled triangle, two small right angled triangles, one square and one parallelogram.
(a) Similarity All pieces are polygons and can be used to form various shapes. All triangles are right angled triangles.
Differences They differ in size (large, small triangles) and shape (triangles, square, parallelogram).
(b) Triangles All triangles have one right angle and two acute angles.
Square All angles are right angles.
Parallelogram It has two acute angles and two obtuse angles. The opposite angles are equal.
(c) Triangles They have three sides of varying lengths.
Square All four sides are of equal length.
Parallelogram Opposite sides are equal in length.
(ii) Do yourself.
Which Shape Am I? (NCERT Pg 100)
Question 20.
Match the statements with appropriate shapes. Do some of them describe more than one shape?
Answer:
(i) (b) This describes a rectangle. A rectangle has four right angles, but its adjacent sides are not necessarily equal in length.
(ii) (c) This describes a rhombus. A rhombus has four equal sides, but its all angles are not equal.
(iii) (c), (d) This describes a parallelogram or a rhombus. Both parallelograms and rhombuses have equal opposite angles and their sides do not necessarily from right angles.
(iv) (d) This describes a parallelogram.
A parallelogram has two pairs of equal and parallel sides and its angles are not necessarily right angles.
(v) (a) This describes a square. A square is a quadrilateral with four equal sides and four right angles.
(vi) (a), (c) This describes a rhombus and square. All of these quadrilaterals have opposite angles that are equal and all sides that are equal.
(vii) (a), (b) This describes a rectangle or a square. Both rectangles and squares have opposite angles that are equal and all angles are right angles.
Kites (NCERT Pg 100)
Question 21.
(i) Make your own kite shape.
(a) Start with a square piece of paper.
(b) Take one corner of the paper and fold it towards the opposite corner, creating a sharp crease along the diagonal.
(c) Open and fold the corner A inwards, aligning the edge with the crease you just made.
(d) Repeat on the other side, folding the other corner B inwards to align with the crease at the centre.
You have a kite shape!
(ii) What shapes do you see in the kite?
Answer:
(i) Do yourself.
(ii) Triangles and quadrilaterals are in the kite.
Play with Circles (NCERT Pg 101)
Question 22.
(i) Do you remember a circle?
(a) Draw a circle with a compass and mark its centre.
(b) Draw its diameter. Mark the endpoints of the diameter.
(c) Draw another diameter of the circle and mark the endpoints.
(d) Now join the four points.
(ii) What shape is formed? Check the sides of the quadrilateral and the angles obtained.
(iii) Try with a different pair of diameters.
(iv) What do you notice about the shape that is formed?
(v) Is it possible to create a 4 -sided shape other than a rectangle through this process?
Answer:
(i) Yes, we remember a circle.
(a) Do yourself.
(b) Do yourself.
(c) Do yourself.
(d) Do yourself.
(ii) A quadrilateral shape is obtained.
(iii) Do yourself.
(iv) If the diameter intersect at right angle, then the shape formed will always be a square otherwise a rectangle.
(v) Yes, square is also possible through this process.
Circle Designs (NCERT Pg 101)
Question 23.
(i) Look at the circle given below. It is marked with points 1 to 24 . Join points 1 to 11,11 to 2,2 to 12 and so on till you reach back at 1. (Try it with different coloured threads on a thick paper or cloth.)
(ii) Can you think of a way to make a design exactly like the image given here? Try to make it.
Answer:
(i) Do yourself.
(ii) Do yourself.
Cube Connections (NCERT Pg 102)
Question 24.
Here are three views of a cube. Can you draw them on the net in the correct order?
Answer:
Question 25.
Here are some big solid cube frames. How many small cubes have been removed from each cube?
Answer:
(i) A large cube is formed by 27 small cubes.
∴ Removed cubes = 1 (center) + 6 (centers of faces) = 7
Hence, 7 small cubes have been removed.
(ii) Here, the large cube is a 4 × 4 × 4 cube, it contains 64 small cubes.
∴ Removed cubes = 32
Hence, 32 small cubes have been removed.
(iii) Here, the large cube is a 5 × 5 × 5 cube, it contains 125 small cubes.
∴ Removed cubes = 81
Hence, 81 small cubes have been removed.
Question 26.
Nisha has glued 27 small cubes together to make a large solid cube. She paints the large cube red. How many of the original small cubes have
(i) three faces painted red? ……….
(ii) two faces painted red? ……….
(iii) one face painted red? ……….
(iv) no faces painted red? ……….
Answer:(i) Three faces painted red -8 cubes
(ii) Two faces painted red -12 cubes
(iii) One faces painted red -6 cubes
(iv) No faces painted red -1 cube
Puzzle (NCERT Pg 102)
Question 27.
Tanu arranged 7 shapes in a line. She used 2 squares, 2 triangles, 1 circle, 1 hexagon and 1 rectangle.
Find her arrangement using the following clues
(a) The square is between the circle and the rectangle.
(b) The rectangle is between the square and the triangle
(c) The two triangles are next to the square.
(d) The hexagon is to the right of the triangle.
(e) The circle is to the left of the square.
Answer:
Icosahedron and Dodecahedron (NCERT Pg 103)
Question 28.
(i) What do these names mean? Once you count their faces, you will know.
Use the nets provided at the end of the book to make icosahedron and dodecahedron models.
(ii) What shapes do you see in an icosahedron and a dodecahedron?
Icosahedron : ………. Dodecahedron: ……….
(iii) Do all the faces look the same?
Icosahedron : ………. Dodecahedron: ……….
(iv) How many faces meet at a vertex (point)?
Icosahedron : ………. Dodecahedron : ……….
(v) Do the same number of faces meet at each vertex?
Icosahedron : ………. Dodecahedron : ……….
(vi) How many edges do you see?
Icosahedron : ………. Dodecahedron : ……….
(vii) How did you count them such that you do not miss out any edge or count an edge twice?
(viii) Can you think of any other solid shapes that have faces that look the same?
(ix) Do the same number of faces meet at each common vertex? ……….
You can also build some 3-D shapes using straws or ice-cream sticks and clay or play dough.
(x) Which shapes did you make?
Answer:
(i) An icosahedrompias 20 trigular faces, while a dodecahedron has 12 pentagonal faces.
(ii) Icosahedron Triangular faces.
Dodecahedron Pentagonal faces.
(iii) Icosahedron Yes, all faces are identical equilateral triangles.
Dodecahedron Yes, all faces are identical regular pentagons.
(iv) Icosahedron 5 faces meet at each vertex.
Dodecahedron 3 faces meet at each vertex.
(v) Icosahedron Yes, 5 faces meet at every vertex.
Dodecahedron Yes, 3 faces meet at every vertex.
(iv) Icosahedron → 30 edges.
Dodecahedron →30 edges.
(vii) One way to count edges without missing or double-counting is to systematically trace each edge, perhaps marking it as we go.
(viii) Yes, other platonic solids like the tetrahedron (equilateral triangles), cube (squares) and octahedron (equilateral triangles) have faces that look the same.
(ix) Yes, the same number of faces meet at each vertex.
(x) Do yourself.