Chapter 4: Basic Geometrical Ideas – Important Questions with Solutions
1. What is a point?
Solution: A point is an exact position or location on a plane surface. It is usually represented by a dot.
2. What is a line segment?
Solution: A line segment is a part of a line that is bounded by two distinct endpoints.
3. Define a ray.
Solution: A ray is a line that starts at one point and extends infinitely in one direction.
4. How many endpoints does a line have?
Solution: A line has no endpoints; it extends infinitely in both directions.
5. What is an angle?
Solution: An angle is formed when two rays meet at a common endpoint called the vertex.
6. How many diagonals does a pentagon have?
Solution: A pentagon has 5 diagonals.
7. What is the sum of all angles in a triangle?
Solution: The sum of the interior angles of a triangle is 180 degrees.
8. What is the area of a rectangle with a length of 8 cm and a width of 5 cm?
Solution: The area of a rectangle is calculated as length × width, which gives 40 square cm.
9. In the figure of a square, if one side is 6 cm, what is the perimeter?
Solution: The perimeter of a square is 24 cm (4 × side length).
10. What is the circumference of a circle with a radius of 7 cm? (Use p = 22/7)
Solution: The circumference is 44 cm (2pr = 2 × 22/7 × 7).
11. What is the area of a triangle with a base of 10 cm and a height of 6 cm?
Solution: The area is 30 square cm (1/2 × base × height).
12. How many degrees are there in a straight angle?
Solution: A straight angle is 180 degrees.
13. How many sides does a hexagon have?
Solution: A hexagon has 6 sides.
14. Name the type of quadrilateral that has only one pair of parallel sides.
Solution: A trapezium (or trapezoid) has only one pair of parallel sides.
15. What is the volume of a cube with side length 4 cm?
Solution: The volume is 64 cubic cm (side³ = 4³).
16. What is a circle?
Solution: A circle is a collection of all points in a plane that are equidistant from a fixed point called the center.
17. What is the radius of a circle?
Solution: The radius is the distance from the center of the circle to any point on the circle.
18. What is a chord in a circle?
Solution: A chord is a line segment joining two points on a circle.
19. Define a quadrilateral.
Solution: A quadrilateral is a polygon with four sides and four angles.
20. What is an equilateral triangle?
Solution: An equilateral triangle is a triangle in which all three sides are of equal length and all three angles are 60 degrees each.
21. What is the perpendicular bisector of a line segment?
Solution: The perpendicular bisector of a line segment is a line that divides the segment into two equal parts at 90 degrees.
22. What is the vertex of an angle?
Solution: The vertex is the point where two rays meet to form an angle.
23. How many diagonals does a square have?
Solution: A square has 2 diagonals.
24. What is the angle sum property of a quadrilateral?
Solution: The sum of all interior angles of a quadrilateral is 360 degrees.
25. How many faces does a cube have?
Solution: A cube has 6 faces.
26. Define a rhombus.
Solution: A rhombus is a quadrilateral where all sides have equal length, and opposite angles are equal.
27. What is a tangent to a circle?
Solution: A tangent is a line that touches a circle at exactly one point.
28. How many edges does a rectangular prism have?
Solution: A rectangular prism has 12 edges.
29. What is a polygon?
Solution: A polygon is a closed figure with three or more straight sides.
30. What are adjacent angles?
Solution: Adjacent angles are two angles that share a common vertex and a common side but do not overlap.
31. What is the centroid of a triangle?
Solution: The centroid is the point where the three medians of a triangle intersect.
32. Define a parallelogram.
Solution: A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel and equal in length.
33. How many degrees are in a complete revolution?
Solution: A complete revolution is 360 degrees.
34. What is the formula to calculate the perimeter of a rectangle?
Solution: The perimeter of a rectangle is 2 × (length + width).
35. What are complementary angles?
Solution: Two angles are complementary if their sum is 90 degrees.
36. What is a parallelogram with all sides equal called?
Solution: A parallelogram with all sides equal is called a rhombus.
37. How many faces does a cylinder have?
Solution: A cylinder has 3 faces – two circular faces and one curved face.
38. Define a trapezium.
Solution: A trapezium (trapezoid) is a quadrilateral with only one pair of parallel sides.
39. What are vertically opposite angles?
Solution: Vertically opposite angles are the angles formed opposite each other when two lines intersect. They are equal.
40. How many diagonals does a hexagon have?
Solution: A hexagon has 9 diagonals.
41. What is the formula to calculate the area of a parallelogram?
Solution: The area of a parallelogram is base × height.
42. What are supplementary angles?
Solution: Two angles are supplementary if their sum is 180 degrees.
43. Define an equilateral polygon.
Solution: A polygon is equilateral if all its sides are of equal length.
44. How many degrees are in a right angle?
Solution: A right angle is 90 degrees.
45. What is the formula to calculate the perimeter of a square?
Solution: The perimeter of a square is 4 × side length.
46. What is the relationship between the radius and diameter of a circle?
Solution: The diameter is twice the radius of a circle (Diameter = 2 × Radius).
47. Define a regular polygon.
Solution: A regular polygon is a polygon where all sides and all angles are equal.
48. How many vertices does a cube have?
Solution: A cube has 8 vertices.
49. What is the circumcenter of a triangle?
Solution: The circumcenter is the point where the perpendicular bisectors of a triangle meet.
50. What are intersecting lines?
Solution: Intersecting lines are lines that meet at a single point.
NCERT Class 6 Mathematics – Basic Geometrical Ideas
51. What is the circumference of a circle?
Solution: The circumference is the distance around a circle, calculated as 2pr (where r is the radius).
52. What is the area of a circle?
Solution: The area of a circle is given by the formula pr² (where r is the radius).
53. Define symmetry.
Solution: Symmetry is a property where one half of an object is a mirror image of the other half.
54. What are complementary angles?
Solution: Two angles are complementary if their sum is 90 degrees.
55. What are supplementary angles?
Solution: Two angles are supplementary if their sum is 180 degrees.
56. How many vertices does a cube have?
Solution: A cube has 8 vertices.
57. What is a scalene triangle?
Solution: A scalene triangle is a triangle in which all three sides have different lengths.
58. What is the area of a triangle?
Solution: The area of a triangle is calculated as (1/2) × base × height.
59. Define a regular polygon.
Solution: A regular polygon is a polygon where all sides and all angles are equal.
60. How many faces does a cube have?
Solution: A cube has 6 faces.
61. What is a right-angled triangle?
Solution: A right-angled triangle is a triangle that has one angle measuring 90 degrees.
62. What is the distance formula?
Solution: The distance formula between two points (x1, y1) and (x2, y2) is v[(x2 – x1)² + (y2 – y1)²].
63. What is the area of a parallelogram?
Solution: The area of a parallelogram is base × height.
64. What is the volume of a cube?
Solution: The volume of a cube is side³.
65. Define a trapezoid.
Solution: A trapezoid is a four-sided figure with at least one pair of parallel sides.
66. What is a chord in a circle?
Solution: A chord is a line segment whose endpoints lie on the circle.
67. How many edges does a cube have?
Solution: A cube has 12 edges.
68. What is the formula for the area of a rhombus?
Solution: The area of a rhombus is (1/2) × d1 × d2 (where d1 and d2 are the lengths of the diagonals).
69. Define a concave polygon.
Solution: A concave polygon is a polygon that has at least one interior angle greater than 180 degrees.
70. What is the formula for calculating the perimeter of a triangle?
Solution: The perimeter of a triangle is the sum of the lengths of its three sides.
71. How do you find the midpoint of a line segment?
Solution: The midpoint can be found by averaging the x-coordinates and y-coordinates of the endpoints.
72. What is a polygon?
Solution: A polygon is a closed figure formed by three or more line segments.
73. Define the term ‘angle of elevation.’
Solution: The angle of elevation is the angle formed by the horizontal line and the line of sight to an object above the horizontal.
74. Define the term ‘angle of depression.’
Solution: The angle of depression is the angle formed by the horizontal line and the line of sight to an object below the horizontal.
75. How do you classify triangles based on their sides?
Solution: Triangles can be classified as equilateral, isosceles, or scalene based on the lengths of their sides.
76. How do you classify triangles based on their angles?
Solution: Triangles can be classified as acute, right, or obtuse based on their angles.
77. What is the sum of interior angles of a triangle?
Solution: The sum of the interior angles of a triangle is 180 degrees.
78. What is a circular sector?
Solution: A circular sector is the area enclosed by two radii of a circle and the arc between them.
79. How many lines of symmetry does a rectangle have?
Solution: A rectangle has 2 lines of symmetry.
80. Define a right prism.
Solution: A right prism is a solid with two identical faces (bases) and rectangular sides connecting them.
81. What is the Pythagorean theorem?
Solution: In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
82. What is the relationship between a radius and a diameter of a circle?
Solution: The diameter is twice the radius (Diameter = 2 × Radius).
83. What is a regular hexagon?
Solution: A regular hexagon is a six-sided polygon with all sides and angles equal.
84. What are the properties of a rectangle?
Solution: A rectangle has opposite sides equal and all angles equal to 90 degrees.
85. What is a 3D shape?
Solution: A 3D shape is an object that has three dimensions: length, width, and height.
86. How many lines of symmetry does a square have?
Solution: A square has 4 lines of symmetry.
87. What is a lateral surface area?
Solution: The lateral surface area is the sum of the areas of the sides of a solid, excluding the bases.
88. Define a segment of a circle.
Solution: A segment of a circle is the area enclosed by a chord and the arc between the endpoints of the chord.
89. What is a quadrilateral?
Solution: A quadrilateral is a polygon with four sides and four angles.
90. How many diagonals does a quadrilateral have?
Solution: A quadrilateral has 2 diagonals.
91. What is a bisector?
Solution: A bisector is a line that divides an angle or a segment into two equal parts.
92. What is a solid figure?
Solution: A solid figure is a three-dimensional object that has length, width, and height.
93. How many edges does a rectangular prism have?
Solution: A rectangular prism has 12 edges.
94. Define a face of a solid.
Solution: A face of a solid is a flat surface that forms part of the boundary of the solid.
95. How many angles are there in a hexagon?
Solution: A hexagon has 6 angles.
96. Define a line of symmetry.
Solution: A line of symmetry is a line that divides a figure into two identical parts.
97. What is an inscribed angle?
Solution: An inscribed angle is formed by two chords in a circle which have a common endpoint.
98. Define a surface area.
Solution: Surface area is the total area of the surface of a three-dimensional object.
99. What is a radius of a circle?
Solution: The radius is the distance from the center of the circle to any point on its circumference.
100. What is a cone?
Solution: A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a point called the apex.