Understanding Shapes-i (polygons)
Class 8th Mathematics RD Sharma Solution
- Draw rough diagram to illustrate the following: (i) Open curve (ii) Closed…
- Classify the following curves as open or closed:
- Draw a polygon and shade its interior. Also draw its diagonals, if any.…
- Illustrate, if possible each one of the following with a rough diagram. (i) A…
- Following are some figures: Classify each of these figures on the basis of the…
- How many diagonals does each of the following have? (i) A convex quadrilateral…
- What is a regular polygon? State the name of a regular polygon of (i) 3 sides…
Exercise 15.1
Question 1.Draw rough diagram to illustrate the following:
(i) Open curve
(ii) Closed curve
Answer:
(i) Open curve
Rough diagram of open curve:
(ii) Closed curve
Rough diagram of close curve:
Question 2.
Classify the following curves as open or closed:
Answer:
Closed curves: (ii), (iii) and (vi)
Open curves: (i), (iv) and (v)
Question 3.
Draw a polygon and shade its interior. Also draw its diagonals, if any.
Answer:
Question 4.
Illustrate, if possible each one of the following with a rough diagram.
(i) A closed curve that is not a polygon.
(ii) An open curve made up entirely of line segments.
(iii) A polygon with two sides.
Answer:
(i) A closed curve that is not a polygon.
(ii) An open curve made up entirely of line segments.
(iii) A polygon with two sides.
A polygon with two sides is not possible.
As we know that a polygon has minimum three sides.
Question 5.
Following are some figures: Classify each of these figures on the basis of the following:
(i) Simple curve (ii) Simple closed curve
(iii) Polygon (iv) Convex polygon
(v) Concave polygon (vi) Not a curve
Answer:
(i) Simple curve
Fig (i), (ii), (v), (vi) and (vii) are simple curves.
Fig (i), (ii), (v), (vi) and (vii) are simple closed curves.
Fig (i) and (ii are polygons. Polygons are minimum three sided enclosed figure.
Fig (ii) is a convex polygon. In a convex polygon all the vertices are pointing outwards.
Fig (i) is a concave polygon. In a concave polygon all the vertices are not pointing outwards.
Fig (viii) is not a curve.
Question 6.
How many diagonals does each of the following have?
(i) A convex quadrilateral
(ii) A regular hexagon
(iii) A triangle
Answer:
(i) A convex quadrilateral
Convex quadrilateral has two diagonals.
(ii) A regular hexagon
An n-sided convex polygon has
diagonals.
∴Applying the above relation for hexagon:
Number of diagonals = 
Regular Hexagon has 9 diagonals.
(iii) A triangle
An n-sided convex polygon has diagonals.
∴Applying the above relation for triangle:
Number of diagonals = 
Therefore a triangle has no diagonal
Question 7.
What is a regular polygon? State the name of a regular polygon of
(i) 3 sides
(ii) 4 sides
(iii) 6 sides
Answer:
(i) 3 sides
Regular Polygon: A regular polygon is an enclosed figure. In a regular polygon minimum sides are three.
(ii) 4 sides
A regular polygon with 4 sides is known as quadrilateral.
(iii) 6 sides
A regular polygon with 6 sides is known as hexagon.