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Question (31)

QN0019522

A square of side 9 cm has area 81 cm². The square on its diagonal has area:

(A) 81 cm²
(B) 108 cm²
(C) 162 cm²
(D) 324 cm²

Correct Answer: C

Explanation:

81 × 2 = 162 cm².

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Question (32)

QN0019523

If the area of a square is x square units, then after one doubling its area becomes:

(A) x/2
(B) x
(C) 2x
(D) 4x

Correct Answer: C

Explanation:

The new square has twice the original area.

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Question (33)

QN0019524

In the paper activity for doubling a square, how many pieces from the second square are arranged around the first square?

(A) 2
(B) 3
(C) 4
(D) 5

Correct Answer: C

Explanation:

Four pieces are arranged around the first square.

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Question (34)

QN0019525

Which of the following cannot be the area of a square obtained by doubling a square of area 7 cm² exactly once?

(A) 14 cm²
(B) 21 cm²
(C) 28 cm²
(D) 56 cm²

Correct Answer: B

Explanation:

Doubling 7 cm² gives 14 cm² only.

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Question (35)

QN0019526

A square of area 100 cm² is doubled twice successively. The final area is:

(A) 200 cm²
(B) 300 cm²
(C) 400 cm²
(D) 800 cm²

Correct Answer: C

Explanation:

100 × 2 × 2 = 400 cm².

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Question (36)

QN0019527

Which of the following statements exactly matches Baudhāyana’s rule?

(A) The side of a square produces double area.
(B) The diagonal of a square produces a square of double the area of the original square.
(C) Doubling the side doubles the area.
(D) The perimeter determines the new square.

Correct Answer: B

Explanation:

This is the exact wording of Baudhāyana’s statement.

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Question (37)

QN0019528

If the area of a square is 50 cm², what is the area after three doublings?

(A) 100 cm²
(B) 200 cm²
(C) 400 cm²
(D) 800 cm²

Correct Answer: C

Explanation:

50 × 2³ = 50 × 8 = 400 cm².

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Question (38)

QN0019529

The sequence of areas formed by repeated doubling of a square starting from area A is:

(A) A, 2A, 4A, 8A
(B) A, 3A, 6A, 9A
(C) A, A², 2A², 4A²
(D) A, A/2, A/4, A/8

Correct Answer: A

Explanation:

Each step doubles the previous area.

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Question (39)

QN0019530

If a square of area 64 cm² is doubled once and then halved once using reverse construction, the final area becomes:

(A) 32 cm²
(B) 64 cm²
(C) 96 cm²
(D) 128 cm²

Correct Answer: B

Explanation:

Doubling and then halving returns the original area.

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Question (40)

QN0019531

Which idea best explains why the square on the diagonal has double the area of the original square?

(A) The diagonal is equal to the side.
(B) The new square contains four congruent triangles while the original contains two.
(C) The perimeter doubles.
(D) The side length doubles.

Correct Answer: B

Explanation:

The doubled square is made of four congruent triangles, whereas the original square has two.

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Question (31)

A square of side 9 cm has area 81 cm². The square on its diagonal has area:

Explanation:

Link:

Question (32)

If the area of a square is x square units, then after one doubling its area becomes:

Explanation:

Link:

Question (33)

In the paper activity for doubling a square, how many pieces from the second square are arranged around the first square?

Explanation:

Link:

Question (34)

Which of the following cannot be the area of a square obtained by doubling a square of area 7 cm² exactly once?

Explanation:

Link:

Question (35)

A square of area 100 cm² is doubled twice successively. The final area is:

Explanation:

Link:

Question (36)

Which of the following statements exactly matches Baudhāyana’s rule?

Explanation:

Link:

Question (37)

If the area of a square is 50 cm², what is the area after three doublings?

Explanation:

Link:

Question (38)

The sequence of areas formed by repeated doubling of a square starting from area A is:

Explanation:

Link:

Question (39)

If a square of area 64 cm² is doubled once and then halved once using reverse construction, the final area becomes:

Explanation:

Link:

Question (40)

Which idea best explains why the square on the diagonal has double the area of the original square?

Explanation:

Link:

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