CBSE Class 3 Mathematics: Chapter 5 Shapes and Designs NCERT Solutions

Solution: Let's count the triangles in each figure carefully:

1. In figure (i), by carefully observing and counting, we can identify 8 distinct triangles.
2. In figure (ii), a systematic count reveals there are 8 triangles.
3. In figure (iii), after a thorough examination, we find there are 9 triangles.

Answer: (a) There are 8 triangles in figure (i), (b) There are 8 triangles in figure (ii), and (c) There are 9 triangles in figure (iii).

Solution: To find the biggest rectangle, we need to visually inspect the provided figures and identify the rectangle that encloses the largest area. The biggest rectangles are highlighted by being enclosed in thick lines in the original figures. Answer: The biggest rectangles are shown enclosed in thick lines in the respective figures.

Solution: The game described seems to be a variation of 'musical chairs' or a similar game played in a circle, where players are eliminated if they don't secure a spot. In the context of the picture, Guddu is not at a corner of the table. In games that involve 'corners' or specific positions, being in the wrong place or not securing a designated spot leads to being out. Answer: Guddu is out because she is not at a corner of the table.

Solution: Observing Guddu's position relative to the table, she is positioned along the side or boundary of the table, not at a distinct corner. This means she is standing against the edge of the table. Answer: Guddu is standing against the edge of the table.

Solution: The game, as described, relies on the presence of 'corners' for players to aim for or be eliminated from. A round table has a continuous, curved edge and does not possess any distinct corners. Therefore, the game cannot be played around a round table because the essential element of corners is missing. Answer: No, this game cannot be played around a round table as it has no corners.

Solution: Let's identify objects around us based on their edges:

Things with straight edges:

• A picture frame
• A book
• A door
• A newspaper
• A blackboard
• A table top

Things with curved edges:

• A ball
• Grapes
• An apple
• A lemon
• A coconut
• A plate

Answer: Examples include: Straight edges - book, door; Curved edges - ball, apple.

Solution: Objects that have straight edges are typically formed by lines meeting at points. These meeting points are called corners or vertices. Therefore, things with straight edges generally do have corners. Answer: Yes, things with straight edges have corners.

Solution: Corners are formed where two or more straight edges meet. Objects that have only curved edges, like a ball or a circular plate, do not have any sharp points or vertices where edges meet. Thus, they do not have corners. Answer: No, things with curved edges have no corners.

Solution: Let's identify some objects that possess both straight and curved edges:

• A bread slice can have straight sides and a curved crust.
• A violin has straight edges along its neck and body, but curved edges around the sound holes and the overall shape.
• An electric guitar also has a mix of straight and curved lines in its design.
• A car has many straight lines in its construction, but also curved surfaces and edges.
• A screw-driver often has a straight shaft but a curved handle.
• A plate with a flat base (straight edge) and a curved rim.

Answer: Examples include a bread slice, a violin, an electric guitar, a car, and a screw-driver.

Solution: This is an instruction to perform a practical activity. Take a standard rectangular sheet of paper, such as A4 size or notebook paper.

Solution: A standard rectangular sheet of paper has four corners. These are the points where the straight edges meet. You can count them by pointing to each vertex. Answer: There are four corners.

Solution: When you take one corner of the rectangular paper and fold it over, you are essentially creating a new edge along the fold line. This fold can either cover up an existing corner or create new ones depending on how it's done. If you fold a corner onto itself, you might obscure one corner but create a new, larger corner shape. If you fold a corner inwards, it can result in 5 corners. Answer: After folding one corner, the paper now has five corners.

Solution: This question refers to the result of folding the paper. The options provided seem to relate to different folding scenarios or perhaps a misunderstanding of the folding process. Let's clarify based on typical folds:

• Folding a corner once, as in the previous question, usually results in 5 corners.
• Achieving exactly 2, 3, or 4 corners might require specific, perhaps multiple, folds or a different interpretation of 'corners'. For instance, folding a rectangle twice in specific ways could lead to a triangle (3 corners) or other shapes. The source's answer suggests specific outcomes for different numbers of folds.

Based on the provided answer options and common paper folding results:

• (i) If a specific fold results in 2 corners (unlikely with simple folds of a rectangle).
• (ii) If a specific fold results in 3 corners (possible, e.g., folding into a triangle).
• (iii) If a specific fold results in 4 corners (possible, e.g., folding in half to make a smaller rectangle).

However, the source's answer seems to list potential outcomes rather than a direct answer to a single fold. Let's assume it refers to different folding possibilities:

• Folding a corner onto itself might result in 6 corners (original 4, minus the folded one, plus 3 new ones from the fold).
• Folding it twice in certain ways could lead to 7 or 8 corners.

Given the ambiguity and the provided answer format, it's best to state the common outcomes:

• Folding one corner typically leads to 5 corners.
• More complex folds can lead to different numbers of corners. The source's answer (6, 7, 8 corners) likely refers to outcomes from multiple or specific types of folds.

Answer: The number of corners obtained by folding can vary. For instance, folding one corner might result in 5 corners. The source indicates possibilities of obtaining 6, 7, or 8 corners through different folding methods.

Solution: Yes, it is possible to fold a rectangular sheet of paper to get exactly three corners using only two folds. If you fold the paper such that two corners meet, and then fold it again along a new edge, you can form a triangle. A triangle is a shape with three straight sides and three corners. Answer: Yes, it can be folded to have three corners by folding it twice. The shape thus obtained is a triangle.

Solution: This instruction asks you to perform the same paper folding activities (counting corners, folding corners) but using a square sheet of paper instead of a rectangular one. A square also has four corners initially.

Solution: Yes, it is possible to fold the corners of a square sheet of paper in a specific way so that the total number of corners remains four. This can be achieved by folding each corner inwards towards the center, creating a smaller square shape. Each fold tucks the corner in without adding new external corners, effectively preserving the four main corners of the resulting shape. Answer: Yes, all the corners of the square sheet can be folded in such a way that the number of corners remains unchanged.

Solution: Let's analyze each item to determine if it has corners and count its edges and corners:

Die: A die is a cube. It has flat faces, straight edges, and sharp corners. It has 6 faces, 12 edges, and 8 corners.

(\checkmark) Yes, it has corners.

Ball: A ball is spherical. It has a continuous curved surface and no flat faces, straight edges, or corners.

Zero edges, Zero corners.

Eraser: A typical eraser is a rectangular prism (cuboid). It has flat faces, straight edges, and sharp corners. It has 6 faces, 12 edges, and 8 corners.

(\checkmark) Yes, it has corners.

Egg: An egg has a smooth, curved shape. It has no flat faces, straight edges, or corners.

Zero edges, Zero corners.

Sheet of paper: A rectangular sheet of paper has flat surfaces and straight edges that meet at corners. It has 4 edges and 4 corners.

(\checkmark) Yes, it has corners.

Completed Table:

Name of things | Number of edges | Whether it has corners | Number of corners

1. Die | 12 | Yes $(\backslash checkmark)$ | 8
2. Ball | 0 | No | 0
3. Eraser | 12 | Yes $(\backslash checkmark)$ | 8
4. Egg | 0 | No | 0
5. Sheet of paper | 4 | Yes $(\backslash checkmark)$ | 4

Answer: The table above shows the items with corners ticked and the counts of edges and corners for each.

Solution: We need to examine each figure provided (though not shown here) and determine if it has corners. Corners are points where straight lines meet. We also need to observe if the figures contain any curved lines.

Based on the provided answer, it is stated that "Yes, these figures have curved lines also." This implies that some figures might have both straight lines forming corners and curved lines within them or as part of their boundary.

To correctly answer, one would:

1. Look at each figure.
2. Identify if there are any points where straight edges meet (corners). Tick those figures. $(\backslash checkmark)$
3. Observe if any part of the figure is made up of curved lines.

Answer: Yes, these figures have curved lines also. The figures with corners should be ticked.

Solution: A figure drawn using only straight lines is a polygon or a combination of line segments. Corners (or vertices) are formed at the points where these straight line segments meet. If you draw any figure using only straight lines, such as a triangle, square, or even an open shape like a 'Z', there will always be points where the lines meet, forming corners. Therefore, it is not possible to draw a figure with no corners using only straight lines. Answer: No, we cannot draw a figure which has no corners using only straight lines.

Solution: This question refers to a Tangram set, which is a dissection puzzle. A standard Tangram set is composed of seven pieces, which are all polygons. Among these seven pieces, there are typically three triangles of different sizes:

• Two large right-angled isosceles triangles.
• One medium right-angled isosceles triangle.
• One small right-angled isosceles triangle.

Therefore, in total, there are three triangles in a standard Tangram set. These triangles are not all equal in size; there are two large ones, one medium one, and one small one. Answer: There are three triangles in the set. No, all of them are not equal in size.