GSEB Class 6 Maths Solutions Chapter 4 Basic Geometrical Ideas Exercise 4.2

Question 1. Classify the following curves as
(i) open or
(ii) closed.
Answer:
(a) This drawing, shaped like a 'Z', shows an open curve.
(b) This blob-like drawing represents a closed curve.
(c) This wavy line drawing is an open curve.
(d) This triangular shape is a closed curve.
(e) This square shape represents a closed curve.
In simple words: Look at each drawing to see if its ends meet up. If the ends connect to form a complete loop, it's a closed curve. If the ends do not meet and there are clear start and finish points, it's an open curve.

Exam Tip: An open curve has distinct start and end points, while a closed curve forms a complete path where the start and end points coincide. Always check if the path is fully enclosed.

Question 2. Draw rough diagrams to illustrate the following:
(a) Open curve
(b) Closed curve
Answer:
(a) An open curve can look like this:

(b) A closed curve can be shown like this:

In simple words: An open curve doesn't have its ends joined, like a partially drawn circle. A closed curve has all its points connected, forming a complete loop or shape, such as a full circle or square.

Exam Tip: When drawing, make sure the open curve clearly shows two distinct end points, and the closed curve has no gaps, forming a continuous boundary.

Question 3. Draw any polygon and shade its interior
Answer: ABCDE represents a polygon, and its inner region is shaded. An example is provided below:

In simple words: Pick any shape with straight sides that connect fully, like a triangle or a square. Then, color in the whole area inside that shape. That colored part is called the interior.

Exam Tip: Remember that a polygon must have straight line segments as sides and must be a closed figure. Shading clearly indicates the interior region.

Question 4. Consider the given figure (a star shape) and answer the questions:
(a) Is it a curve?
(b) Is it closed?
Answer:
(a) Yes, this specific drawing is considered a curve.
(b) Yes, this figure also forms a closed curve.
In simple words: A curve is any line that isn't perfectly straight. Since the star shape is drawn with lines, it's a curve. Also, because all its lines connect up and there are no open ends, it's a closed curve.

Exam Tip: Even if a figure has straight line segments, it is considered a curve in geometry. For it to be closed, all segments must connect to form a continuous boundary without any breaks.

Question 5. Illustrate, if possible, each one of the following with a rough diagram:
(a) A closed curve that is not a polygon.
(b) An open curve made up entirely of line segments.
(c) A polygon with two sides.
Answer:
(a) A closed curve that is not a polygon (for instance, a circle or an irregular loop with bends):
This shape forms a complete loop, but it is not a polygon as polygons are constructed solely from straight line parts.
(b) An open curve formed completely from straight line segments:

(c) It is not possible to form a polygon with just two sides.
In simple words: (a) You can draw a bumpy, closed loop that doesn't use straight lines—that's a closed curve, but not a polygon. (b) For an open curve with only straight lines, imagine drawing half a square or a zig-zag that doesn't connect. (c) You can't make a polygon with just two sides because a polygon always needs three or more straight sides to enclose a space.

Exam Tip: Remember that polygons are always closed figures formed by straight line segments. A curve can be closed without being a polygon if it contains curved parts. An open curve will always have distinct start and end points.