Word Problems: Perimeter and Area | Mathematics for Class 6 PDF Download

Q1: Priya has two rectangular tables with areas of 12 m² and 15 m². Their dimensions are 4 m by 3 m and 5 m by 3 m, respectively. She wants a third table with an area of 18 m² and a length of 6 m. What is the breadth of Priya’s third table?

Ans:
Area = length × breadth.
Given area = 18 m² and length = 6 m.
6 × breadth = 18 → breadth = 18 ÷ 6 = 3 m.
The breadth of Priya’s third table is 3 m.

Q2: Suman has two squares: Square A with an area of 36 square units and Square B with an area of 49 square units. Which square has a larger perimeter?

Ans:
Side of Square A = √36 = 6 units. Perimeter of Square A = 4 × 6 = 24 units.
Side of Square B = √49 = 7 units. Perimeter of Square B = 4 × 7 = 28 units.
Since 28 units > 24 units, Square B has the larger perimeter (28 units).

Q3: Sneha is calculating the area of a parallelogram-shaped plot with a base of 9 m and a height of 4 m. What is the area of the plot?

Ans:
Area of a parallelogram = base × height.
Area = 9 × 4 = 36 m².
The area of Sneha’s plot is 36 m².

Q4: Vikram uses a wire to form a regular hexagon-shaped frame with a perimeter of 48 cm. What is the length of each side of the hexagon?

Ans:
A regular hexagon has 6 equal sides. Perimeter = 6 × side length.
48 = 6 × side length → side length = 48 ÷ 6 = 8 cm.
Each side of Vikram’s hexagon is 8 cm long.

Q5: Neha has a square with a side length of 5 m. She creates a new square by tripling the side length. What is the perimeter of the new square?

Ans:
Original side = 5 m. New side = 5 × 3 = 15 m.
Perimeter of the new square = 4 × side = 4 × 15 = 60 m.
The perimeter of Neha’s new square is 60 m.

Q6:  Arjun wants to paint a rectangular wall that is 8 m long and 5 m high. The cost of painting is ₹50 per square meter. What will be the total cost?

Ans:
Area of the wall = length × height = 8 × 5 = 40 m².
Cost = area × cost per m² = 40 × ₹50 = ₹2,000.
The total cost for Arjun to paint the wall is ₹2,000.

Q7: Shalini has two rectangles: Rectangle X with dimensions 12 cm by 5 cm and Rectangle Y with dimensions 9 cm by 8 cm. Which rectangle has a larger perimeter?

Ans:
Perimeter of Rectangle X = 2(12 + 5) = 2 × 17 = 34 cm.
Perimeter of Rectangle Y = 2(9 + 8) = 2 × 17 = 34 cm.
Both rectangles have the same perimeter. Each perimeter is 34 cm.

Q8: By splitting the figure into rectangles , find the area of the following figure(in cm)

Ans: 

1. Left tall rectangle

• This rectangle is at the left side and its height is 3 units.

• Its width is 1 unit (marked at the bottom left).

• Dimensions = 1 × 3.

• Area = 1 × 3 = 3 cm².

2. Right tall rectangle

• By symmetry, the rectangle on the right side also has width 1 unit and height 3 units.

• (The bottom-right mark shows its width is 1.)

• Dimensions = 1 × 3.

• Area = 1 × 3 = 3 cm².

3. Top middle rectangle

• Between the two tall side rectangles there is a small rectangle at the top.

• Its width across is 3 units (marked on the top inner line).

• Its height is 1 unit.

• Dimensions = 3 × 1.

• Area = 3 × 1 = 3 cm².

Total Area = 3 cm² + 3 cm² + 3 cm² = 9 cm².

Q9: Anjali has two rectangles: Rectangle A with dimensions 14 cm by 6 cm, and Rectangle B with dimensions 10 cm by 8 cm. What is the difference in their perimeters?

Ans:
Perimeter of Rectangle A = 2(14 + 6) = 2 × 20 = 40 cm.
Perimeter of Rectangle B = 2(10 + 8) = 2 × 18 = 36 cm.
Difference = 40 − 36 = 4 cm.
The difference in perimeters is 4 cm.

Q10: Meena has a rectangular garden that is 20 m long and 10 m wide. She builds a path around the garden that is 2 m wide on all sides. What is the perimeter of the outer edge of the path?

Ans:
Outer length = 20 + 2 + 2 = 24 m.
Outer width = 10 + 2 + 2 = 14 m.
Perimeter of outer edge = 2(24 + 14) = 2 × 38 = 76 m.
The perimeter of the path’s outer edge is 76 m.