NCERT Solutions for Class 5th Maths Chapter 7 Which regular shapes fit around a point — Find Out
Book page 94 Updated on2026-09-19
Q1.
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.)
Answer
Yes, they fit perfectly. Six triangles fit around one point.
Six corners of 60 make one full turn. No gap is left and no triangle sits on another.
Corner of an equilateral triangle = 60 How many make a full turn? 360 ÷ 60 = 6 Check: 60 × 6 = 360 ✓
Why it happens: A triangle with all three sides equal also has all three angles equal, and each of them is 60. Six of these corners together make exactly one complete turn, so the triangles close up with nothing left over. That is why equilateral triangles tessellate.
Did you notice? The six triangles together make a regular hexagon. That is why hexagon tiles and triangle tiles look so good side by side.
Q2.
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?
Answer
Yes, squares fit together with no gap and no overlap. You need 4 squares.
Four square corners fit round a point exactly. Nothing is left over and nothing overlaps.
Corner of a square = a right angle = 90 360 ÷ 90 = 4 squares Check: 90 × 4 = 360 ✓
Why it happens: Every corner of a square is a right angle. Four right angles make a complete turn — think of turning a quarter turn four times to face the front again. So four squares close up exactly, and squares tessellate.
Look around you: The tiles on your classroom floor, a chess board, the squares on graph paper — all of them are squares fitting together four at a corner.
Q3.
Can five squares fit together around a point without any gaps or overlaps? Why or why not?
Answer
No. Five squares cannot fit around a point. The fifth one has to climb on top of the others.
Four squares already fill the turn: 90 × 4 = 360 Five squares would need: 90 × 5 = 450 450 is bigger than 360 by 90 So one whole right angle has nowhere to go.
There is no room left for a fifth square, so it overlaps the others.
Why it happens: Around any point there is exactly one full turn to share out, and that is 360. Four square corners of 90 use it all up. A fifth corner needs another 90, and there is simply none left.
The same rule everywhere: Shapes fit round a point only when their corners add up to exactly 360 — not less (gap) and not more (overlap).
Q4.
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
Yes. Three regular hexagons fit around a point.
Three regular hexagons meet at every point — the same shape a honeycomb makes.
Corner of a regular hexagon = 120 360 ÷ 120 = 3 hexagons Check: 120 × 3 = 360 ✓
Why it happens: A regular hexagon can be cut into 6 equal triangles from its centre, and each corner of the hexagon is made of two 60 angles. That makes 120 at each corner, and three of them make a full turn. So regular hexagons tessellate.
Did you know? Honeybees build their comb out of hexagons. Hexagons hold the most honey for the least wax, and they leave no gaps at all.