Worksheet Solutions: Perimeter and Area of Plane Figures | Mathematics Class 6 ICSE PDF Download

A. Multiple Choice Questions

Q1. The perimeter of a rectangle with length l and breadth b is:
(a) l + b 
(b) 2l + b 
(c) l + 2b 
(d) 2(l + b)
Ans: (d) 2(l + b)
Sol: Rectangle perimeter is the sum of all sides: l + b + l + b = 2(l + b).

Q2. A square has side 8 cm. Its perimeter is:
(a) 16 cm 
(b) 24 cm 
(c) 32 cm 
(d) 64 cm
Ans: (c) 32 cm
Sol: Perimeter of a square = 4 × side = 4 × 8 = 32 cm.

Q3. An equilateral triangle has side 9 cm. Its perimeter is:
(a) 18 cm 
(b) 27 cm 
(c) 36 cm 
(d) 45 cm
Ans: (b) 27 cm
Sol: Perimeter of equilateral triangle = 3 × side = 3 × 9 = 27 cm.

Q4. Which of the following is a correct unit of area?
(a) cm (b) m (c) cm² (d) km
Ans: (c) cm²
Sol: Area is measured in square units (cm², m², km²).

Q5. A square’s area is 81 cm². Its perimeter is:
(a) 18 cm 
(b) 27 cm 
(c) 36 cm 
(d) 81 cm
Ans: (c) 36 cm
Sol: Side = √81 = 9 cm; Perimeter = 4 × 9 = 36 cm.

B. Short Answer Questions

Q6. Find the perimeter of a quadrilateral with side lengths 7 cm, 9 cm, 6 cm, and 8 cm.
Ans: 30 cm
Sol: Add all sides: 7 + 9 + 6 + 8 = 30 cm.

Q7. The perimeter of a square garden is 1.2 m. Find the length of each side (in cm).
Ans: 30 cm
Sol: Side = Perimeter ÷ 4 = 1.2 ÷ 4 = 0.3 m = 30 cm.

Q8. Find the area of a rectangle with length 13 cm and breadth 9 cm.
Ans: 117 cm²
Sol: Area = length × breadth = 13 × 9 = 117 cm².

Q9. A rectangle has area 84 cm² and breadth 7 cm. Find its length and perimeter.
Ans: Length 12 cm; Perimeter 38 cm
Sol: Length = Area ÷ Breadth = 84 ÷ 7 = 12 cm.
Perimeter = 2(l + b) = 2(12 + 7) = 38 cm.

Q10. Convert 2.5 m to cm. Then find the perimeter of a rectangle with length 2.5 m and breadth 80 cm (answer in cm).
Ans: 500 cm
Sol: 2.5 m = 250 cm. Perimeter = 2(l + b) = 2(250 + 80) = 2 × 330 = 660 cm.
(If they only asked conversion: 2.5 m = 250 cm. If both: perimeter is 660 cm.)

C. Long Answer Questions

Q11. The perimeter of a rectangular field is 94 m. The length of the field is twice its breadth plus 5 m. Find the length, breadth, and area of the field.
Ans: Step 1: Perimeter = 94 → Length + Breadth = 47

Step 2: Let breadth = b. Then length = 2b + 5.
So, (2b + 5) + b = 47
3b + 5 = 47
3b = 42
b = 14 m

Step 3: Length = 2(14) + 5 = 28 + 5 = 33 m

Step 4: Area = 33 × 14 = 462 m²

Q12. A rectangular room is 6 m long and 4 m wide. Square tiles of side 20 cm are used to cover the floor. How many tiles are needed to cover the floor completely?

Ans: Convert dimensions to cm: 6 m = 600 cm, 4 m = 400 cm.

• Area of floor = 600 × 400 = 240,000 cm².

• Area of one tile = 20 × 20 = 400 cm².

• Number of tiles = 240,000 ÷ 400 = 600 tiles.

Q13.  A rectangle has length 30 m and breadth 10 m.
(a) Find its perimeter and area.
(b) Make a square with the same perimeter. Find its side and area.
(c) Compare the areas. Which shape encloses more area with the same boundary length?
Ans:
(a) Perimeter 80 m; Area 300 m²
(b) Square side 20 m; Area 400 m²
(c) Square has greater area (400 m² vs 300 m²)
Sol (stepwise):

1. Rectangle perimeter = 2(l + b) = 2(30 + 10) = 80 m.
   Rectangle area = l × b = 30 × 10 = 300 m².

2. Same perimeter for square: 4 × side = 80 → side = 80 ÷ 4 = 20 m.
   Square area = side × side = 20 × 20 = 400 m².

3. Compare: 400 m² > 300 m².
   With the same perimeter, the square encloses more area than this rectangle.