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Question (1)

QN0029533

A rectangular playground is 48 m long and 32 m wide. A triangular stage is constructed inside it using the entire width of the playground as the base and one of the longer sides as its height. What fraction of the playground remains uncovered by the stage?

(A) 1/4
(B) 1/2
(C) 3/4
(D) 2/3

Correct Answer: B

Explanation:

Area of rectangle = 48 × 32 = 1536 m². Area of triangle = ½ × 48 × 32 = 768 m². Remaining fraction = 768/1536 = 1/2.

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Question (2)

QN0029534

Which statement is always true for two triangles drawn on the same base and between the same parallel lines?

(A) Their perimeters are equal.
(B) Their areas are equal.
(C) Their heights are different.
(D) They are congruent.

Correct Answer: B

Explanation:

Triangles on the same base and between the same parallel lines have the same base and height, so their areas are equal.

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Question (3)

QN0029535

A parallelogram has a base of 18 cm and an area of 198 cm². If another side of the parallelogram is taken as the base and measures 22 cm, what is the corresponding height?

(A) 9 cm
(B) 10 cm
(C) 11 cm
(D) 12 cm

Correct Answer: A

Explanation:

Height = Area ÷ Base = 198 ÷ 22 = 9 cm.

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Question (4)

QN0029536

The diagonals of a rhombus are doubled while keeping the shape a rhombus. The new area becomes

(A) 2 times
(B) 3 times
(C) 4 times
(D) 8 times

Correct Answer: C

Explanation:

Area of a rhombus = ½ × d₁ × d₂. Doubling both diagonals makes the area four times.

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Question (5)

QN0029537

A trapezium has parallel sides 18 cm and 30 cm with height 12 cm. A rectangle has the same height and the same area. What is the length of the rectangle?

(A) 18 cm
(B) 22 cm
(C) 24 cm
(D) 30 cm

Correct Answer: C

Explanation:

Area of trapezium = ½ × (18 + 30) × 12 = 288 cm². Rectangle length = 288 ÷ 12 = 24 cm.

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Question (6)

QN0029538

A quadrilateral is divided into two triangles of areas 42 cm² and 58 cm² by one of its diagonals. What is the area of the quadrilateral?

(A) 84 cm²
(B) 90 cm²
(C) 100 cm²
(D) 116 cm²

Correct Answer: C

Explanation:

Area of quadrilateral = Sum of the areas of the two triangles = 42 + 58 = 100 cm².

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Question (7)

QN0029539

Which of the following figures can always be converted into a rectangle of equal area by cutting and rearranging its parts?

(A) Parallelogram
(B) Rhombus
(C) Trapezium
(D) All of these

Correct Answer: D

Explanation:

All these figures can be converted into rectangles of equal area by dissection methods.

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Question (8)

QN0029540

A triangular flower bed has base 20 m and height 16 m. If the cost of planting grass is ₹45 per square metre, what is the total cost?

(A) ₹6,400
(B) ₹7,000
(C) ₹7,200
(D) ₹7,500

Correct Answer: C

Explanation:

Area = ½ × 20 × 16 = 160 m². Cost = 160 × 45 = ₹7,200.

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Question (9)

QN0029541

A rectangle and a parallelogram have the same base and the same height. Which statement is correct?

(A) Rectangle has greater area.
(B) Parallelogram has greater area.
(C) Both have equal areas.
(D) Their areas cannot be compared.

Correct Answer: C

Explanation:

Area of both figures = Base × Height.

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Question (10)

QN0029542

A square has side 14 cm. Its diagonals divide it into four triangles of equal area. What is the area of each triangle?

(A) 24.5 cm²
(B) 49 cm²
(C) 98 cm²
(D) 196 cm²

Correct Answer: B

Explanation:

Area of square = 14 × 14 = 196 cm². Each of the four triangles has area = 196 ÷ 4 = 49 cm².

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Question (1)

A rectangular playground is 48 m long and 32 m wide. A triangular stage is constructed inside it using the entire width of the playground as the base and one of the longer sides as its height. What fraction of the playground remains uncovered by the stage?

Explanation:

Link:

Question (2)

Which statement is always true for two triangles drawn on the same base and between the same parallel lines?

Explanation:

Link:

Question (3)

A parallelogram has a base of 18 cm and an area of 198 cm². If another side of the parallelogram is taken as the base and measures 22 cm, what is the corresponding height?

Explanation:

Link:

Question (4)

The diagonals of a rhombus are doubled while keeping the shape a rhombus. The new area becomes

Explanation:

Link:

Question (5)

A trapezium has parallel sides 18 cm and 30 cm with height 12 cm. A rectangle has the same height and the same area. What is the length of the rectangle?

Explanation:

Link:

Question (6)

A quadrilateral is divided into two triangles of areas 42 cm² and 58 cm² by one of its diagonals. What is the area of the quadrilateral?

Explanation:

Link:

Question (7)

Which of the following figures can always be converted into a rectangle of equal area by cutting and rearranging its parts?

Explanation:

Link:

Question (8)

A triangular flower bed has base 20 m and height 16 m. If the cost of planting grass is ₹45 per square metre, what is the total cost?

Explanation:

Link:

Question (9)

A rectangle and a parallelogram have the same base and the same height. Which statement is correct?

Explanation:

Link:

Question (10)

A square has side 14 cm. Its diagonals divide it into four triangles of equal area. What is the area of each triangle?

Explanation:

Link:

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