Worksheet Solutions: Fundamental Concept of Geometry | Mathematics Class 6 ICSE PDF Download

A. Multiple Choice Questions (MCQs)

Q1. Which of the following has no length, no width, and no thickness?
(a) Line
(b) Point
(c) Plane
(d) Ray

Ans: (b) Point
Sol: A point only shows a location. It has no size.

Q2. A line segment AB is 12 cm long. If point C is its midpoint, then AC =?
(a) 3 cm
(b) 6 cm
(c) 9 cm
(d) 12 cm

Ans: (b) 6 cm
Sol: Midpoint divides a segment into 2 equal parts → 12 ÷ 2 = 6 cm.

Q3. In a rectangle, opposite sides are equal and each angle = ?
(a) 45°
(b) 60°
(c) 90°
(d) 180°

Ans: (c) 90°
Sol: By definition, all corners of a rectangle are right angles (90°).

Q4. In a circle with centre O and radius 5 cm, the length of diameter is:
(a) 5 cm
(b) 7 cm
(c) 10 cm
(d) 25 cm

Ans: (c) 10 cm
Sol: Diameter = 2 × radius = 2 × 5 = 10 cm.

Q5. Lines l and m are in the same plane and do not intersect. They are called:
(a) Intersecting lines
(b) Parallel lines
(c) Concurrent lines
(d) Opposite rays

Ans: (b) Parallel lines
Sol: Parallel lines never meet and remain equidistant.

B. Short Answer Questions

Q6. A line segment AB is 14 cm long. Point C divides it into two parts such that AC = 9 cm. Find the length of CB.
Ans: 5 cm
Sol: AB = 14 cm. Since AC = 9 cm, CB = AB – AC = 14 – 9 = 5 cm.

Q7. A square park has each side = 25 m. Find the perimeter of the park.
Ans: 100 m
Sol: Perimeter = 4 × side = 4 × 25 = 100 m.

Q8. In triangle XYZ, side XY = 6 cm, YZ = 8 cm, and XZ = 10 cm.
(a) Is this a closed figure?
(b) Verify whether XY + YZ > XZ.

Ans:
(a) Yes, it is a triangle (closed figure).
(b) XY + YZ = 6 + 8 = 14 > 10 = XZ → condition satisfied.

Sol:
A triangle is a closed figure formed by 3 line segments. For validity, the sum of any two sides must be greater than the third side. Here the condition holds true.

Q9. A line AB passes through points A(2,0) and B(8,0). Find the length of AB.
Ans: 6 units
Sol: Distance = 8 – 2 = 6 units (on a straight line).

Q10. Identify which figure has a curvilinear boundary and which has a linear boundary:
(i) Circle
(ii) Rectangle

Ans: Circle – Curvilinear; Rectangle – Linear.
Sol: Circle’s edge is curved, rectangle’s edges are straight.

C. Long Answer Questions

Q11. A rectangular playground has length = 40 m and breadth = 25 m.
(a) Find its perimeter.
(b) Find its area.
(c) Identify one pair of parallel and one pair of perpendicular sides.

Ans:
(a) Perimeter = 2 × (40 + 25) = 130 m
(b) Area = 40 × 25 = 1000 sq.m
(c) Parallel: length sides (40 m each); Perpendicular: length side and breadth side.

Sol:

1. Rectangle has opposite sides equal → apply perimeter and area formulas.

2. In a rectangle, opposite sides are parallel, adjacent sides meet at 90°.

Q12. A circular pond has radius 7 m.
(a) Find its diameter.
(b) A point A is 7 m away from the centre – where is A located?
(c) A point B is 4 m away from centre – where is B located?
(d) A point C is 10 m away – where is C located?

Ans:
(a) Diameter = 14 m
(b) A – On boundary
(c) B – Inside circle
(d) C – Outside circle

Sol:

• Diameter = 2 × radius

• Compare distances with radius:

  • Equal → boundary

  • Less → inside

  • Greater → outside

Q13. Three towns A, B, C are on a road. Distance AB = 15 km, BC = 10 km, AC = 25 km.
(a) Are the towns collinear?
(b) Is B between A and C?

Ans: Yes, collinear; Yes, B lies between A and C.
Sol:

On a line: AB + BC = AC.

15 + 10 = 25 → condition satisfied. Hence collinear with B in between