NCERT Solutions for Class 4th Maths Chapter 1 Hidden shapes, dividing shapes and cutting shapes — Puzzling Shapes
Book page 19–20 Updated on2026-09-19
Q1.
Identify the hidden shapes and write their names.
The tangle of red lines printed in the book.
Answer
Follow one red line at a time with your finger until it comes back to
where it started. Five shapes are hidden in the tangle.
a circle — on the left, a closed round curve;
a cylinder — standing upright, with an oval at the top, an oval at the
bottom and two straight lines joining them;
a square — on the right, an upright four-sided shape with all sides
equal;
a rectangle — a slanting four-sided shape, long on two sides and short on
the other two;
a triangle — a three-sided shape near the top.
Tip: Trace the picture on a fresh sheet and go over one shape at
a time with a coloured pencil. Shapes that cross each other then become easy to see.
Why it happens: Our eyes lose track where the lines cross. Naming
the shape by the number of its sides — 3 sides, 4 sides, or a curve — makes it
easy again.
Q2.
Draw 2 lines to divide the triangle into 1 square and 2 triangles.
The triangle drawn on the dot grid in the book.
Answer
Use the middle point of the slanting side. The two lines both end
there.
The triangle has a square corner at the top left. Its two straight sides are each
4 dots long.
Find the middle dot of the slanting side — it is 2 dots along from each end.
Line 1: from that middle dot, draw straight up to the top side, meeting it 2
dots from the corner.
Line 2: from the same middle dot, draw straight across to the left side,
meeting it 2 dots below the corner.
You now have 1 square at the top-left corner and
2 triangles, one on each side of it.
The same triangle with the two cuts drawn in.
Why it happens: Both new lines are 2 dots long, and they
meet the two sides at right angles. Four right angles with equal sides make a square, and
the two leftover pieces have 3 sides each.
Q3.
Draw 2 lines to divide the square into 3 triangles.
The square drawn on the dot grid in the book.
Answer
Draw one diagonal first, then one more line inside.
Line 1: join the top-left corner to the bottom-right corner. The square is
now cut into 2 triangles.
Mark the middle point of that line — it is the centre of the square.
Line 2: join the top-right corner to that middle point. This cuts the upper
triangle into 2 smaller triangles.
After line 1: 2 triangles
Line 2 cuts one of them in two: 2 – 1 + 2 = 3 triangles
The same square with the two cuts drawn in.
Try This: Line 2 can go from the top-right corner to
any point on the diagonal, not only the middle. You still get 3 triangles.
Why it happens: A straight cut across a triangle always makes
two triangles out of it, if it starts at a corner. So one extra cut turns 2 triangles
into 3.
Q4.
Draw lines to show the cuts needed on the shapes in the left column to get the smaller shapes on the right. (A) (B) (C)
The three rows (A), (B) and (C): the big shape on the left and the small shapes on the right.
Answer
Count the small shapes on the right first — that tells you how many
pieces the cuts must make.
(A) six-sided shape → 1 rectangle and 2 triangles
Draw 2 straight lines going up and down, one at each place where the
pointed end begins.
The middle piece is the rectangle; the two pointed ends are the triangles.
(B) square → 4 triangles
Draw 1 line straight down the middle of the square. It becomes 2 tall
rectangles.
Draw a corner-to-corner line inside each of those rectangles.
That is 3 lines in all, and they make 4 triangles.
(C) triangle → 1 triangle, 1 six-sided shape and 2 small triangles
Draw 1 line across the top, cutting off the pointed top as a triangle.
Draw 1 short line at the bottom-left corner and 1 at the bottom-right corner,
cutting off a small triangle at each.
That is 3 lines, and the piece left in the middle has 6 sides.
The same shapes with the cutting lines drawn in.
Why it happens: Every straight cut adds one more piece.
Cutting a corner off a shape always adds one more side to the piece left behind — that
is how a triangle with its three corners cut off becomes a six-sided shape.