Hard Level Worksheet

Very Short Answer Questions (1 Mark Each)

(1) Write the formula for the area of a rectangle in terms of its length l and breadth b.

Correct! The area of a rectangle = length × breadth = l × b.

(2) Find the side of a square whose area is 196 cm2.

Perfect! Side = Area = 196 = 14 cm.

(3) The perimeter of a rectangle is 64 cm. If its length is 20 cm, find its breadth.

Excellent! Breadth = (Perimeter ÷ 2) - length = (64 ÷ 2) - 20 = 12 cm.

(4) Write the unit of perimeter in SI system.

Great! The SI unit of perimeter is metre (m).

(5) Find the perimeter of a square whose area is 81 cm2.

Correct! Side = 81 = 9 cm. Perimeter = 4 × 9 = 36 cm.

Short Answer Questions (2 Marks Each)

Answer each question clearly

(1) A square park has an area of 625 m2. Find the length of its side and its perimeter.

Side: m Perimeter: m

Excellent! Side = 625 = 25 m, Perimeter = 4 × 25 = 100 m.

(2) A rectangle has length 18 cm and breadth 12 cm. Find its area and perimeter.

Area: cm2 Perimeter: cm

Perfect! Area = 18 × 12 = 216 cm2, Perimeter = 2(18 + 12) = 60 cm.

(3) The perimeter of a square is 72 cm. Find its area.

Correct! Side = 72 ÷ 4 = 18 cm. Area = 18 × 18 = 324 cm2.

(4) A rectangular garden has length 45 m and breadth 30 m. Find the cost of fencing it at ₹25 per metre.

Great! Perimeter = 2(45 + 30) = 150 m. Cost = 150 × 25 = ₹3,750.

(5) A rectangular hall measures 24 m × 18 m. Find the number of square tiles of side 3 m needed to cover the floor.

Perfect! Hall area = 24 × 18 = 432 m2. Tile area = 3 × 3 = 9 m². Number of tiles = 432 ÷ 9 = 48.

Long Answer Questions (4 Marks Each)

(1) A square playground has side 60 m. Inside it, a square lawn of side 40 m is left for grass. Find the area of the remaining ground.

Area of remaining ground: m2

Correct! Playground area = 60 × 60 = 3600 m2. Lawn area = 40 × 40 = 1600 m2. Remaining = 3600 - 1600 = 2000 m2.

(2) A rectangular park is 80 m long and 60 m wide. A path 5 m wide is constructed around the park outside. Find the area of the path.

Area of path: m2

Perfect! Total area = (80+10) × (60+10) = 90 × 70 = 6300 m2. Park area = 80 × 60 = 4800 m2. Path area = 6300 - 4800 = 1400 m2.

(3) A farmer has a square field of side 50 m. He wants to dig a square pond of side 20 m inside the field. Find the area of the remaining field.

Area of remaining field: m2

Excellent! Field area = 50 × 50 = 2500 m2. Pond area = 20 × 20 = 400 m2. Remaining = 2500 - 400 = 2100 m2.

(4) A hall is 40 m long and 30 m wide. How many square carpets of side 5 m are required to cover the entire hall?

Great! Hall area = 40 × 30 = 1200 m2. Carpet area = 5 × 5 = 25 m2. Number of carpets = 1200 ÷ 25 = 48.

(5) A rectangular field is twice as long as it is wide. If its perimeter is 180 m, find its length, breadth, and area.

Breadth: m Length: m Area: m2

Correct! Let breadth = x, length = 2x. Perimeter = 2(x + 2x) = 6x = 180, so x = 30. Area = 60 × 30 = 1800 m2.

Part B: Objective Questions (1 Mark Each)

Choose the correct answer and write the option (a/b/c/d)

(1) The area of a square whose side is 15 cm is:

(a) 225 cm2 (b) 30 cm2 (c) 60 cm2 (d) 45 cm2

Correct! Area = 15 × 15 = 225 cm2.

(2) A rectangle has length 50 m and breadth 20 m. Its area is:

(a) 100 m2 (b) 1,000 m2 (c) 1,500 m2 (d) 5,000 m2

Correct! Area = 50 × 20 = 1,000 m2.

(3) If the area of a square is 144 cm2, its perimeter is:

(a) 24 cm (b) 36 cm (c) 48 cm (d) 12 cm

Correct! Side = 144 = 12 cm. Perimeter = 4 × 12 = 48 cm.

(4) The length of a rectangle is 40 m and breadth is 30 m. Its perimeter is:

(a) 70 m (b) 100 m (c) 140 m (d) 200 m

Correct! Perimeter = 2(40 + 30) = 2(70) = 140 m.

(5) A rectangular hall has length 12 m and breadth 9 m. The number of square tiles of side 3 m needed to cover the floor is:

(a) 12 (b) 16 (c) 20 (d) 24

Correct! Hall area = 12 × 9 = 108 m2. Tile area = 3 × 3 = 9 m2. Number of tiles = 108 ÷ 9 = 12.

(6) The cost of fencing a square park of side 25 m at ₹30 per metre is:

(a) ₹ 1,500 (b) ₹ 2,000 (c) ₹ 3,000 (d) ₹ 5,000

Correct! Perimeter = 4 × 25 = 100 m. Cost = 100 × 30 = ₹ 3,000.

(7) A square field has perimeter 80 m. Its area is:

(a) 200 m2 (b) 400 m2 (c) 600 m2 (d) 1,000 m2

Correct! Side = 80 ÷ 4 = 20 m. Area = 20 × 20 = 400 m2.

(8) A rectangular playground has length 90 m and breadth 60 m. Its area is:

(a) 1,800 m2 (b) 2,400 m2 (c) 4,500 m2 (d) 5,400 m2

Correct! Area = 90 × 60 = 5,400 m2.

(9) The perimeter of a rectangle whose length = 25 cm and breadth = 15 cm is:

(a) 50 cm (b) 60 cm (c) 70 cm (d) 80 cm

Correct! Perimeter = 2(25 + 15) = 2(40) = 80 cm.

(10) The side of a square is doubled. Its area becomes:

(a) Double (b) Triple (c) Four times (d) Half

Correct! If side = a, area = a2. If side = 2a, area = 2a2 = 4a2.

True or False

Determine whether these statements are True or False:

Quiz

🎉 Congratulations! What You've Mastered:

You have successfully completed the "Expert Mensuration" worksheet and learned:

(1) Expert Formula Mastery: Applying complex formulas with confidence and precision

(2) Square Root Applications: Finding dimensions using square root calculations expertly

(3) Multi-step Problem Solving: Handling complex scenarios with paths, ponds, and remaining areas

(4) Advanced Algebraic Reasoning: Solving problems with dimensional relationships and constraints

(5) Complex Cost Calculations: Computing expenses for large-scale projects and materials

(6) Sophisticated Area Problems: Managing inner/outer areas, overlapping regions, and composite shapes

(7) Professional Problem Analysis: Breaking down complex real-world scenarios systematically

(8) Expert Unit Conversions: Working confidently with SI units and large measurements

(9) Advanced Reverse Calculations: Finding unknown parameters from given area or perimeter

(10) Real-world Engineering Applications: Solving problems involving construction, landscaping, and space planning

Exceptional work! You have mastered advanced mensuration and can handle complex engineering and architectural problems!