NCERT Solutions for Class 7th Maths Chapter 6 Figure it Out — Tiling
Book page 156 Updated on2026-09-19
Q1.
How can the tangram pieces be rearranged to form each of the following figures?
The seven tangram pieces, page 155
The seven tangram pieces (page 155) and the ten figures to be made from them (page 156).
Answer
Every one of the ten silhouettes uses all seven pieces, exactly once, with no gaps and no overlaps — that is what makes a tangram a tiling problem.
Piece
Shape
Area (square = 16 units)
A, B
Two large right triangles
4 + 4 = 8
F
One medium right triangle
2
C, E
Two small right triangles
1 + 1 = 2
D
One square
2
G
One parallelogram
2
Total
16 = the whole square ✓
A method that works for all ten.
Place the two large triangles A and B first. They are half the total area, so they must fill the biggest blocks of the silhouette — the body of the fish, the two long strokes of the M, the two halves of the boat's hull.
Look for the right angles and the long straight edges of the outline. A large triangle's hypotenuse is the longest straight edge available, so any very long straight side of the silhouette is almost certainly one of them.
Fit the medium triangle F next, then the square D and the parallelogram G into the square-ish and slanted regions.
Keep the two small triangles C and E for last — they are the ears of the fox, the beak of the duck, the tail fin of the fish, the head and hands of the running figure.
Remember the parallelogram G may need to be flipped over, not just turned. It is the only piece with no mirror symmetry.
Why it happens: the seven pieces always add up to the same area, so every tangram picture has exactly the area of the original square. That is a useful check: if your arrangement leaves a hole, a piece is in the wrong place, because the total area cannot change however you rearrange it.
Tip: cut the seven pieces out of thick card. Trace round the printed silhouette at full size first, then slide the pieces about on top of the tracing — it is far faster than guessing on paper.