How many practice questions are available for Mensuration?

SparkEd Math offers 60+ practice questions for Mensuration across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

Is Mensuration content free on SparkEd Math?

Yes! All Mensuration content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Mensuration differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Mensuration problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Mensuration content aligned with the Olympiad syllabus?

Yes, all Mensuration questions and lessons on SparkEd Math are fully aligned with the Mathematical Olympiad Preparation (Olympiad) syllabus for Class 6. The content follows the official curriculum structure and exam pattern.

Mensuration — Class 6 Olympiad (2025-26)

About Mensuration — Class 6 Olympiad

Calculate perimeter and area of basic shapes; solve composite figure problems requiring creative decomposition. This topic is part of the Olympiad Class 6 mathematics syllabus (chapter: Module 9). On this page you can practice 50 questions across three difficulty levels — 20 easy, 20 medium, and 10 hard — each with a visual step-by-step solution, plus a timed 27-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Mensuration — solved examples for Class 6 Olympiad

Example 1easy

A square-shaped garden has an area of 144 square meters. If a gardener wants to put a decorative border around its entire edge, what will be the total length of the border?

A)12 m
B)48 m
C)36 m
D)24 m

Step-by-step solution

Let 's' be the side length of the square. The area of a square is s × s. Given area = 144 m².
Since 12 × 12 = 144, the side length 's' = 12 m.
The perimeter of a square is 4 × s.
Perimeter = 4 × 12 m = 48 m.

Answer: 48 m

Example 2medium

A rectangular park has a length that is three times its width. If the cost of fencing the park at ₹15 per meter is ₹1800, what is the area of the park?

A)300 m²
B)432 m²
C)675 m²
D)720 m²

Step-by-step solution

Total cost of fencing = ₹1800, cost per meter = ₹15. So, Perimeter = Total cost / Cost per meter = 1800 / 15 = 120 meters.
Let the width of the park be 'w' meters. Then the length 'l' is 3w meters. The perimeter of a rectangle is 2(l + w).
Substituting the values: 2(3w + w) = 120 => 2(4w) = 120 => 8w = 120 => w = 15 meters. So, l = 3 × 15 = 45 meters.
Area of the park = length × width = 45 m × 15 m = 675 m².

Answer: 675 m²

Example 3hard

A large square sheet of paper has a side length of 10 cm. Four identical smaller squares, each of side length 2 cm, are cut out from its corners. Additionally, a square hole of side length 2 cm is cut out from the exact center of the sheet. What is the perimeter of the final remaining paper?

A)40 cm
B)44 cm
C)48 cm
D)52 cm

Step-by-step solution

The original perimeter of the large square sheet is 4 × 10 cm = 40 cm.
When identical squares are cut from the corners of a larger square, the outer perimeter of the remaining shape remains unchanged. Each corner cut removes two segments and adds two equal segments to the boundary.
A square hole cut from the center, however, adds its entire perimeter to the total perimeter of the remaining paper. The perimeter of the central square hole is 4 × 2 cm = 8 cm.
Therefore, the total perimeter of the final remaining paper is the original outer perimeter plus the perimeter of the central hole: 40 cm + 8 cm = 48 cm.

Answer: 48 cm

Practice questions on Mensuration

Q1.easy
A rectangular swimming pool has a perimeter of 50 meters. If its length is 15 meters, what is the area of the pool?
1. A)150 sq m
2. B)100 sq m
3. C)180 sq m
4. D)120 sq m
Show answer
Answer: 150 sq m
Hint: Use the perimeter formula to find the width first, then calculate the area.
Q2.easy
Three identical squares, each with a side length of 5 cm, are joined side-by-side to form a single long rectangle. What is the perimeter of this new rectangle?
1. A)60 cm
2. B)50 cm
3. C)40 cm
4. D)45 cm
Show answer
Answer: 40 cm
Hint: When squares are joined, some sides become internal and don't contribute to the perimeter of the new shape.
Q3.easy
A rectangular cardboard sheet measures 20 cm by 15 cm. A rectangular hole of 8 cm by 5 cm is cut out from its center. What is the area of the remaining cardboard?
1. A)260 sq cm
2. B)280 sq cm
3. C)240 sq cm
4. D)220 sq cm
Show answer
Answer: 260 sq cm
Hint: Calculate the area of the whole sheet first, then subtract the area of the cutout.
Q4.medium
A square paper sheet has a side length of 20 cm. From each of its four corners, a smaller square of side 3 cm is cut out. What is the area of the remaining paper sheet?
1. A)364 cm²
2. B)376 cm²
3. C)388 cm²
4. D)392 cm²
Show answer
Answer: 364 cm²
Hint: Calculate the area of the original square, then find the total area of the four small squares that are removed.
Q5.medium
Two rectangular fields, A and B, have the same area. Field A has a length of 40 m and a width of 25 m. Field B has a length of 50 m. What is the difference between the perimeters of Field A and Field B?
1. A)8 m
2. B)10 m
3. C)12 m
4. D)15 m
Show answer
Answer: 10 m
Hint: First, calculate the area of Field A. Since Field B has the same area, use it to find the width of Field B. Then calculate both perimeters.
Q6.medium
A gardener wants to lay a rectangular lawn of dimensions 24 m by 18 m. He plans to leave a uniform path of 1.5 m width all around the lawn. What is the area of the path?
1. A)108 m²
2. B)117 m²
3. C)126 m²
4. D)135 m²
Show answer
Answer: 126 m²
Hint: Find the dimensions of the lawn including the path. The area of the path will be the difference between the total area (lawn + path) and the area of the lawn.
Q7.hard
A square of side 12 cm is drawn. Inside this square, a smaller square is formed by connecting the midpoints of the sides of the larger square. What is the area of the region between the outer square and the inner square?
1. A)36 sq cm
2. B)72 sq cm
3. C)108 sq cm
4. D)144 sq cm
Show answer
Answer: 72 sq cm
Hint: Think about the four triangles formed at the corners when the inner square is drawn.
Q8.hard
A rectangular field has its length 3 times its breadth. The cost of fencing this field at a rate of ₹15 per meter is ₹1800. What is the area of the field?
1. A)540 sq m
2. B)600 sq m
3. C)630 sq m
4. D)675 sq m
Show answer
Answer: 675 sq m
Hint: First, use the total fencing cost and rate to find the perimeter. Then, use the length-breadth relationship to find the dimensions.
Q9.hard
A solid metal cube of side 8 cm has a rectangular hole (cuboid) of dimensions 4 cm × 2 cm × 8 cm drilled completely through its center, from one face to the opposite face. What is the volume of the remaining metal?
1. A)448 cubic cm
2. B)464 cubic cm
3. C)480 cubic cm
4. D)496 cubic cm
Show answer
Answer: 448 cubic cm
Hint: Calculate the volume of the original cube and the volume of the material removed by the hole.

These are 9 of the 50 questions available for Mensuration. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.