7TH MATHS PERIMETER AND AREA OF THE SQUARE

HOME (NMMS)

MAIN PAGE-MATHS

Area of a Square – Advanced MCQ Quiz

1. If a square has a side length of 's', which of the following expressions does NOT represent its area?

a) s × s b) s squared c) 4 × s d) length × width

Correct Answer: c) 4 × s

Explanation: The expression 4 × s calculates the Perimeter (the outer boundary) of a square, not the Area (the space inside). Because a square's length and width are identical (s), options a, b, and d all correctly result in the area.

2. A square piece of paper has a total perimeter of 20 cm. What is the total area of the space it covers?

a) 20 cm² b) 400 cm² c) 25 cm² d) 100 cm²

Correct Answer: c) 25 cm²

Explanation: First, find the side length. Perimeter = 4 × side, so 20 = 4 × side. The side length is 5 cm. Then, find the Area: 5 cm × 5 cm = 25 cm².

3. The area of a square playground is exactly 64 square meters. If a student runs along exactly three edges of this playground, how far did they run?

a) 8 m b) 32 m c) 24 m d) 64 m

Correct Answer: c) 24 m

Explanation: If Area = 64 m², then one side length is 8 m (since 8 × 8 = 64). If the student runs along 3 edges, they run 8 + 8 + 8 = 24 meters.

4. A square floor with an area of 100 m² is to be covered with square tiles. If each tile has an area of 1 m², how many tiles are required to line just one edge of the floor?

a) 100 b) 10 c) 40 d) 50

Correct Answer: b) 10

Explanation: The area of the floor is 100 m², meaning its side length is 10 m. Since each tile is 1 m² (meaning it has a side of 1 m), it takes exactly 10 tiles to fit along the 10 m edge.

5. If you decrease the side length of a square by exactly half, what happens to its total area?

a) It is halved b) It becomes one-third c) It becomes one-fourth d) It remains the same

Correct Answer: c) It becomes one-fourth

Explanation: Let's use an example: If a side is 4 cm, the area is 16 cm². If you halve the side to 2 cm, the new area is 2 × 2 = 4 cm². The new area (4) is exactly one-fourth (1/4) of the original area (16).

6. A square with a side length of 6 cm is mathematically "reshaped" into a rectangle. If the width of the new rectangle is 4 cm, what must its length be to maintain the exact same area?

a) 24 cm b) 9 cm c) 36 cm d) 10 cm

Correct Answer: b) 9 cm

Explanation: The area of the square is 6 cm × 6 cm = 36 cm². Since the rectangle has the same area (36 cm²) and a width of 4 cm, we find the length by dividing Area by Width: 36 ÷ 4 = 9 cm.

7. A farmer has a square field with an area of 121 m². He wants to build a fence around it, but one entire side borders a deep river and needs no fencing. What length of fence does he need to buy?

a) 44 m b) 22 m c) 33 m d) 48 m

Correct Answer: c) 33 m

Explanation: Since the area is 121 m², each side of the square is 11 m (11 × 11 = 121). A full perimeter would be 4 sides (44 m), but he only needs to fence 3 sides because of the river. 11 m + 11 m + 11 m = 33 m.