7TH MATHS MEASUREMENTS - PERIMETER AND AREA OF SQUARE AND RECTANGLE

🧮 Area & Perimeter of Squares and Rectangles – Master Quiz

1. If you walk exactly once around the boundary of a square park, which mathematical expression represents the total distance covered?

a) side × side b) 4 × side c) side + side d) 2 × side

Correct Answer: b) 4 × side
Walking around the boundary means finding the perimeter. A square has 4 equal sides, so the total distance is side + side + side + side, which simplifies to 4 × side.

2. A wire is bent to form a square. If each side of this square frame measures exactly 60 mm, what is the total length of the wire in centimeters?

a) 36 cm b) 12 cm c) 24 cm d) 18 cm

Correct Answer: c) 24 cm
First, convert mm to cm: 60 mm = 6 cm. The total length of the wire is the perimeter of the square. Perimeter = 4 × 6 cm = 24 cm.

3. A carpenter is framing a rectangular portrait. Which expression correctly calculates the total length of the wooden border needed?

a) length × breadth b) length + breadth c) 2 × (length + breadth) d) length × 2 + breadth

Correct Answer: c) 2 × (length + breadth)
A rectangle has two equal lengths and two equal breadths. Adding them all up gives Length + Length + Breadth + Breadth, which is mathematically grouped as 2 × (length + breadth).

4. A rectangular swimming pool is 7 meters long. Its width is exactly 3 meters shorter than its length. What is its total perimeter?

a) 28 m b) 22 m c) 30 m d) 32 m

Correct Answer: b) 22 m
Length = 7 m. Width = 7 - 3 = 4 m. Perimeter = 2 × (7 + 4) = 2 × 11 = 22 m.

5. When measuring the amount of fencing needed to surround a garden, which of these units is geometrically appropriate?

a) m b) m² c) m³ d) kg

Correct Answer: a) m
Fencing surrounds a boundary, which is a 1-dimensional measurement (Perimeter). Therefore, standard linear units like meters (m) are used. Square units (m²) are for area, and cubic units (m³) are for volume.

6. The total perimeter of a square tile is 40 cm. What is the measure of a single edge?

a) 8 cm b) 10 cm c) 12 cm d) 15 cm

Correct Answer: b) 10 cm
Perimeter = 4 × side. If 40 = 4 × side, then side = 40 ÷ 4 = 10 cm.

7. The side of a square plot measures 5.5 m. What is its perimeter?

a) 22 m b) 11 m c) 27.5 m d) 33 m

Correct Answer: a) 22 m
Perimeter = 4 × side. 4 × 5.5 m = 22 m.

8. To find out how much artificial turf is required to completely cover a square field, which formula must be used?

a) length × width b) 4 × side c) side × side d) side + side

Correct Answer: c) side × side
Covering the surface of a field requires calculating its Area. The area of a square is calculated by multiplying the length of its side by itself (side × side).

9. A square chessboard has a side length of 5 cm. What is its total surface area?

a) 10 cm² b) 25 cm² c) 20 cm² d) 5 cm²

Correct Answer: b) 25 cm²
Area = side × side. 5 cm × 5 cm = 25 cm².

10. A square painting covers an area of 64 cm² on a wall. What is the length of one of its sides?

a) 6 cm b) 7 cm c) 8 cm d) 9 cm

Correct Answer: c) 8 cm
Area = side × side. You need to find a number that, when multiplied by itself, equals 64. 8 × 8 = 64, so the side length is 8 cm.

11. The area of a square plot is 100 m². What is its side length?

a) 9 m b) 10 m c) 11 m d) 12 m

Correct Answer: b) 10 m
Area = side × side. Since 10 × 10 = 100, the side length is 10 m.

12. If an architect decides to double the side lengths of a square foundation, how will the new area compare to the original?

a) Twice b) Four times c) Three times d) Half

Correct Answer: b) Four times
Let the original side be 's' (Area = s²). If doubled, the new side is '2s'. The new Area is (2s) × (2s) = 4s², which is exactly four times the original area.

13. A square with a side of 6 cm has the exact same area as a certain rectangle. Which of the following could be the dimensions of that rectangle?

a) 3 cm × 12 cm b) 4 cm × 10 cm c) 5 cm × 6 cm d) 6 cm × 10 cm

Correct Answer: a) 3 cm × 12 cm
First, find the area of the square: 6 cm × 6 cm = 36 cm². Now find the matching rectangle area. 3 cm × 12 cm = 36 cm². (The others equal 40, 30, and 60).

14. A square garden has an area of 121 m². How many meters of wire are required to fence it completely around the boundary?

a) 22 m b) 44 m c) 36 m d) 48 m

Correct Answer: b) 44 m
Step 1: Find the side. Area = 121 m², so side = 11 m (since 11×11 = 121).
Step 2: Find the perimeter (fencing). 4 × 11 m = 44 m.

15. A rectangle's length is 9 cm and its breadth is 6 cm. What is its perimeter?

a) 30 cm b) 25 cm c) 20 cm d) 15 cm

Correct Answer: a) 30 cm
Perimeter = 2 × (length + breadth). 2 × (9 + 6) = 2 × 15 = 30 cm.