GSEB Class 6 Maths Solutions Chapter 5 Understanding Elementary Shapes Exercise 5.8

Question 1. Examine whether the following are polygons. If any one among them is not, say why?
Answer:
(a) No, this figure is not a polygon. It is an open shape that consists of curved lines, not straight line segments.
(b) Yes, this figure is a polygon with six sides.
(c) A circle is not formed by straight line segments, so it is not considered a polygon.
(d) This shape is not formed only by straight line segments and is also open, so it is not a polygon.
In simple words: A polygon must be a closed shape made only of straight lines. We check each figure to see if it meets these two rules. Figures (a), (c), and (d) do not, while (b) does.

Exam Tip: Remember the two key criteria for a polygon: it must be a closed figure, and it must consist only of straight line segments. Any shape that fails either of these conditions is not a polygon.

Question 2. Name each polygon. Make two more examples of each of these.
Answer:
(a) This figure is a quadrilateral.
(b) This figure is a triangle.
(c) This figure is a pentagon.
(d) This figure is an octagon.

Other examples:

Two quadrilaterals:

Two triangles:

Two pentagons:

Two octagons:

Exam Tip: The name of a polygon is determined by its number of sides. Learning prefixes like "quad-" (4), "tri-" (3), "penta-" (5), and "octa-" (8) helps quickly identify polygon types.

Question 3. Sketch of a regular hexagon. Connecting any three of its vertices, draw a triangle. Identify the type of the triangle you have drawn.
Answer:ABCDEF is a regular hexagon. When we join its alternate vertices A, C, and E, we get triangle ACE. This triangle is a regular triangle. Therefore, the triangle created is an equilateral triangle.
In simple words: We start with a hexagon where all sides and angles are equal. If you pick every other corner and connect them, you'll draw a triangle. This triangle will have all its sides equal, making it an equilateral triangle.

Exam Tip: A "regular" polygon means all sides are equal and all interior angles are equal. When forming triangles by connecting alternate vertices in a regular polygon, often specific types of triangles (like equilateral or isosceles) are formed, which can be deduced from the polygon's symmetry.

Question 4. Draw a rough sketch of a regular octagon. (Use squared paper if you wish). Draw a rectangle by joining exactly four of the vertices of the octagon.
Answer:ABCDEFGH is a regular octagon. When we join vertices G and D, we get the line segment GD. Similarly, by joining H and C, we get the line segment HC. As a result, we form the rectangle CDGH. We can also get other diagonals by connecting any two vertices. For example, by connecting A, F, B, and E, we can form another rectangle, ABEF.
In simple words: Draw a shape with eight equal sides and eight equal angles. If you then connect four specific corners (like C, D, G, and H, or A, B, E, and F), you can make a perfect rectangle inside the octagon.

Exam Tip: When drawing geometric figures like octagons, ensure all sides appear equal and all angles appear consistent for a 'regular' figure. For inscribed shapes, be precise about which vertices are connected to form the required figure.

Question 5. A diagonal is a line segment that joins any two vertices of the polygon and is not a side of the polygon. Draw a rough sketch of a pentagon and draw its diagonals.
Answer: A diagonal is a line segment that connects any two vertices of a polygon, but it is not one of its sides.The diagonals formed are \( \overline{\mathrm{AC}} \), \( \overline{\mathrm{AD}} \), \( \overline{\mathrm{BD}} \), \( \overline{\mathrm{BE}} \) and \( \overline{\mathrm{CE}} \).
In simple words: Draw a five-sided shape. Then, connect every corner to all other corners, but do not draw lines that are already sides of the pentagon. These new lines inside the pentagon are its diagonals.

Exam Tip: To draw diagonals correctly, choose one vertex and draw lines to all non-adjacent vertices. Repeat this for all vertices, being careful not to draw the same diagonal twice. For a pentagon, there are 5 diagonals.