NCERT Solutions for Class 5th Maths Chapter 7 Naming the seven pieces and building shapes with them — Tangram
Book page 99 Updated on2026-09-19
Q1.
Look at the tangram set given at the end of your textbook. Cut out all the shapes. Name them.The tangram set given at the end of the textbook.
Answer
A tangram is one square cut into 7 pieces. Here they are, with their names.
How many
Name of the piece
Number of sides
2
Large triangle
3
1
Medium triangle
3
2
Small triangle
3
1
Square
4
1
Parallelogram
4
7
in all
5 triangles + 2 four-sided pieces
Five of the seven pieces are triangles. The other two are a square and a parallelogram.
Handle with care: Cut along the printed lines slowly, and keep all 7 pieces in one envelope. If even one piece is lost, most of the puzzles cannot be made.
Q2.
How are they same or different from each other?
Answer
Same: five of the seven pieces are triangles, and all five are exactly the same shape — a right-angled triangle with two equal sides. Different: they come in three sizes, and two pieces are not triangles at all.
What is the same
What is different
All 5 triangles have one square corner
They come in 3 sizes — large, medium, small
All 5 triangles have 2 equal sides
The square and the parallelogram have 4 sides, not 3
Every corner in the whole set is 45, 90 or 135
The square has 4 equal sides; the parallelogram does not
The 2 large pieces match each other; so do the 2 small ones
The medium triangle, the square and the parallelogram cover the same amount of space, but look different
2 large triangles are equal to each other 2 small triangles are equal to each other 1 medium triangle = 1 square = 1 parallelogram = 2 small triangles (same amount of space) 1 large triangle = 4 small triangles
Why this matters for the puzzles: Because the medium triangle, the square and the parallelogram all cover the same space, you can often swap one for another. That is why the same picture can be made in more than one way.
Check it yourself: Place the two small triangles on top of the square piece, and then on top of the medium triangle. Each time they cover it exactly.
Q3.
What do you notice about the angles of each of the shapes?The tangram set given at the end of the textbook.
Answer
Every corner in the whole tangram set is one of only three sizes: 45, 90 or 135.
Piece
Its angles
Total
Every triangle (all 5)
90, 45, 45
180
Square
90, 90, 90, 90
360
Parallelogram
45, 135, 45, 135
360
How to see it without a protractor
Take the corner of a sheet of paper — that is a right angle, 90.
Fit it into the biggest corner of any triangle. It matches exactly.
Now fold that paper corner in half. The new corner is 45.
Fit it into the two sharp corners. Both match, so both are 45.
For the parallelogram's blunt corner, hold the paper right angle plus the folded 45 together — 90 + 45 = 135. It matches.
Why only these three sizes: The whole tangram is cut from one square. Every cut is either along a side or along a diagonal, and a diagonal cuts a right angle exactly in half. So every angle in the set is 90, or half of it (45), or one and a half of it (135).
Handy fact: 45 + 45 = 90, and 45 + 135 = 180. That is why tangram pieces slot together so neatly along straight edges.
Q4.
What do you notice about the sides of each of the shapes?The tangram set given at the end of the textbook.
Answer
Every triangle has 2 equal sides. The square has all 4 sides equal. The parallelogram has its opposite sides equal.
Piece
What its sides look like
Name for that
All 5 triangles
two short sides equal, one long slanting side
Isosceles right triangle
Square
all four sides equal
Square
Parallelogram
opposite sides equal, adjacent sides not
Parallelogram
There is one more thing to notice, and it is the secret of the whole puzzle:
The slanting side of a small triangle is exactly as long as the short side of the medium triangle.
The slanting side of the medium triangle is exactly as long as the short side of a large triangle.
The side of the square equals the short side of a small triangle.
Why the pieces always fit: Because so many sides are exactly the same length, a piece can be laid flat against another with no gap. If the lengths did not match, the tangram would not work at all.
Check it yourself: Line up the slanting side of a small triangle against the short side of the medium triangle. They end at the same place.
Q5.
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.The four shapes to be made, page 99.
Answer
The four outlines in the book are a parallelogram, a rectangle, a triangle and a trapezium. Here is one way to make each.
Four target shapes, four simple solutions. Other solutions exist — try to find them.
Steps for each one
Triangle: Take the two large triangles. Put a short side of one exactly against a short side of the other, like a mirror. You get a bigger triangle.
Parallelogram: Take the same two large triangles, but turn one of them half a turn before joining. Now you get a parallelogram.
Rectangle: Join the two small triangles along their long slanting sides — they make a small square. Put that beside the square piece.
Trapezium: Put the square piece in the middle. Stand one small triangle against its left side and one against its right side, both sloping outwards.
Try more: Every one of these can also be made using all 7 pieces. That is much harder — a good challenge for a rainy afternoon.