**NCERT Solutions for Class 3 Mathematics Chapter-5 Shapes and Designs**

**Have Fun with Shapes**

**1. How many triangles are there in the following figures?**

**Answer:** (a) There are 8 triangles in figure (i)

(b)There are 8 triangles in figure (ii)

(c)There are 9 triangles in figure (iii).

**2. Find the biggest rectangle in the figures given below:**

**Answer:** Biggest rectangles in the figures are shown enclosed in thick lines.

**Edges and Corners**

**1. (a)Looking at the picture given above, can you tell who is out?**

** (b)Where is Guddu standing?**

** (c) Can this game be played around a round table? Why?**

**Answer:** (a) Guddu is out as she is not at a comer of the table.

(b)Guddu is standing against the edge of the table.

(c)No, this game cannot be played around a round table as it has no corners.

**2. (a) Look around you and identify things with straight and curved edges?**

** (b)Do the things with straight edges have corners?**

** (c)Do the things with curved edges have corners?**

** (d)Try to find things which have both straight and curved edges.**

**Answer:** (a) Following things have straight edges; picture, book, door, newspaper, blackboard.

Following things have curved edges; ball, grapes, apple, lemon, coconut.

(b)Yes, things with straight edges have comers.

(c)No, things with curved edges have no corners.

(d)Following things have both straight and curved edges; bread, violin, electric guitar, car, screw-driver.

**Activity Time**

**1. Take a rectangular sheet of paper.**

** 2. Count its corners.**

** 3. Now fold one of its corners.**

** (a)How many corners does it have now?**

** (b)How many comers will you get by folding?**

** (i)2 cpmers, (ii) 3 comers, (iii) 4 corners.**

** (c)Can you fold this paper in such a way that it has only three comers? You are allowed only two folds. What shape will you get?**

** 4. Repeat the activity with a square sheet of paper.**

** 5. Can you fold all the corners of the square sheet in such a way that the number of corners remains unchanged?**

**Answer:** 1. Do as directed.

2. There are four corners.

3. (a) Five comers.

(b)(i) 6 comers, (ii) 7 comers, (iii) 8 corners.

(c)Yes, it can be folded to have three corners by folding it twice. The shape thus obtained is a triangle.

4. Do as directed.

5. Yes, all the corners of the square sheet can be folded in such a way that the number of corners remains unchanged.

**3.**

**Answer:** Yes, these figures have curved lines also.

**4. Using only straight lines, can you draw a figure which has no corners?**

**Answer: **No, we cannot draw a figure which has no corners; using straight lines.

**Tangram**

**1. How many triangles do you have in your set? Are all of them equal in size? Find**

** If out.**

**Answer:** There are three triangles in the set. No, all of them are not equal in size. These triangles are numbered as 1, 2, 3, 4, and 5 in the tangram.

**2. Use the two small triangles in the tangram set to get the following shapes:**

**Answer: **The given shapes can be made as under by using two small triangles numbered 2 and 5 in the tangram are shown below:

**3. Which two pieces of the tangram set are exactly same? Find out.**

**Answer:** The two pieces numbered 2 and 5 of the tangram set are exactly the same.

**4. Find matching sides among the following pairs of pieces:**

** (a)Pieces 1 and 2 (b)Pieces 2 and 4**

** (c)Pieces 1 and 5 (d)Pieces 2 and 5**

**Answer:** (a) Longest side of piece 2 with the smaller side of piece 1.

(b) Smaller side of piece 2 with the smaller side of piece 4 and the longest side of piece 2 with the longest side of piece 4.

(c)Longest side of piece 5 with the smaller side of piece 1.

(d)Longer side of piece 2 with the longer side of piece 5 and smaller side of piece 2 with the smaller side of piece 5.

**The 7-piece Tangram**

**Here is the picture of a seven-piece tangram.**

** You can cut out these pieces and put them together in different ways to make some very interesting shapes.**

**Try making these shapes:**

** 1. Now try making the following shapes using only the pieces written here:**

**Answer:** Shapes using the desired pieces are shown against them as under:

**Weaving Patterns**

**Golu and Binu went to the market with their aunt. They saw many rugs (durries).**

** 1. Which geometrical shapes can you identify in these borders? Draw them in your notebook.**

**Answer:** The geometrical shapes used in these borders are:

**2. Is any shape repeating in a particular pattern? Which ones?**

**Answer:** Yes, many shapes are repeating in a particular manner such as:

**3. Are the shapes made of**

** (i) Curved lines (ii) Straight lines**

** (iii) Both curved and straight lines.**

**Answer:** Shapes are made of both curved and straight lines.

**4. Look at your cloths, your mother’s saris/shawls, rugs and mats. Can you identify some patterns? Draw them in your notebook.**

**Answer:** Make two or three designs that usually appear on cloths, your mother’s series/ shawls, rugs, and mats.

**5. Complete the following tiling pattern.**

**Answer:** Complete pattern is as under:

**6. Complete this pattern. Compare it with the pattern on page 70 which also uses six sided shapes. What is the difference between the two?**

**Answer:** Here hexagons are interconnected with each other sides directly whereas here two triangles appear between the hexagons.

**7. Khushboo and Hariz live in Agra. One day they went to see the Taj Mahal. The floor had the pattern shown below:**

**What do you think? Discuss with your friends.**

**Answer: **I think only one type of tile has been used but their placements differ.