NCERT Solutions for Class 4th Maths Chapter 1 A pentagon of straws, a circle of straws, and drawing a circle with a scale — Let Us Make
Book page 16 Updated on2026-09-19
Q1.
Try to make this 5-sided shape with all sides equal (Pentagon). Are these right angles?
The straw pentagon shown in the book — five equal straws joined with clay.
Answer
No. None of the five angles is a right angle.
Cut 5 straws of the same length.
Join them end to end with small lumps of clay to make a closed 5-sided shape.
Put your paper right angle checker on each corner.
The checker does not fit — every corner is wider than the
checker. So all five angles are obtuse angles.
Why it happens: A pentagon has to close up with only five
corners. If its corners were right angles, the sides would turn too sharply and the
shape would close after four sides, making a square instead.
Q2.
Does the shape of the pentagon change if we gently push one of its sides. Yes/No How does this change the angles?
The straw pentagon shown in the book — five equal straws joined with clay.
Answer
Yes. The pentagon changes its shape at once.
The five straws stay exactly as long as before.
Some corners close up and become smaller; the corners next to them
open out and become bigger.
A corner may even become a right angle, or an acute angle, if you push far
enough.
Why it happens: Only the triangle is rigid. Any shape with more
than three sides can change its angles while keeping the same side lengths, so a
pentagon bends out of shape as soon as it is pushed.
Try this: Join two straws across the pentagon from corner to
corner. It is now made of triangles, and it stops bending.
Q3.
Can you make a circle using straws? Look at the picture. The lengths of the straws in this picture are …………. (Equal/Unequal)
The picture of straws laid out from one centre.
Answer
The lengths of the straws are Equal.
All the straws start from the same point in the middle.
Each straw is exactly as long as every other one.
So all their outer ends stop at the same distance from the middle, and together
those ends make a circle.
Why it happens: A circle is the set of all points that are at the
same distance from one centre point. Equal straws from one centre mark out exactly those
points.
Q4.
What will happen if we take straws of unequal lengths?
The picture of straws laid out from one centre.
Answer
The outer ends will no longer lie on a circle.
A long straw reaches far out; a short straw stops close to the middle.
Joining the ends then gives a bumpy, uneven curve — in and out, in and out.
It will look like a star or a flower, not like a circle.
Why it happens: A shape is a circle only when every point of its
border is the same distance from the centre. Unequal straws break that rule.
Q5.
Can you use a scale to draw a circular shape? Let us see. Mark a point A. Draw many points that are at an equal distance from point A. Connect the dots freehand. What do you get? ................
Point A with many points marked at an equal distance from it.
Answer
You get a circle.
Mark a point and name it A.
Choose a length, say 3 cm.
Put the zero of the scale on A, turn the scale a little, and mark a point at 3 cm.
Do this again and again, all the way round A.
When you have many such points, join them freehand.
The curve that comes out is a circle. The point A is its centre,
and the line from the centre to the border is the radius.
Every marked point is 3 cm from A.
So the radius of this circle = 3 cm
Why it happens: Marking points at one fixed distance from A is
exactly the rule that makes a circle. The more points you mark, the smoother the circle
looks.