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Question (11)

QN0029543

A rhombus has diagonals 24 cm and 18 cm. A parallelogram has the same area and a base of 27 cm. What is the corresponding height of the parallelogram?

(A) 6 cm
(B) 7 cm
(C) 8 cm
(D) 9 cm

Correct Answer: C

Explanation:

Area of rhombus = ½ × 24 × 18 = 216 cm². Height = 216 ÷ 27 = 8 cm.

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Question (12)

QN0029544

A rectangular sheet measures 40 cm × 25 cm. Four identical right triangles, each of area 25 cm², are cut from its corners. What is the area of the remaining sheet?

(A) 800 cm²
(B) 850 cm²
(C) 900 cm²
(D) 950 cm²

Correct Answer: C

Explanation:

Area of rectangle = 40 × 25 = 1000 cm². Area removed = 4 × 25 = 100 cm². Remaining area = 900 cm².

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Question (13)

QN0029545

A trapezium has parallel sides in the ratio 3 : 5. If their sum is 64 cm and the height is 10 cm, what is its area?

(A) 280 cm²
(B) 300 cm²
(C) 320 cm²
(D) 340 cm²

Correct Answer: C

Explanation:

Area of trapezium = ½ × (sum of parallel sides) × height = ½ × 64 × 10 = 320 cm².

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Question (14)

QN0029546

A triangle and a parallelogram stand on the same base and have the same height. If the area of the triangle is 54 cm², what is the area of the parallelogram?

(A) 54 cm²
(B) 81 cm²
(C) 96 cm²
(D) 108 cm²

Correct Answer: D

Explanation:

Area of parallelogram = 2 × Area of triangle = 2 × 54 = 108 cm².

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Question (15)

QN0029547

A square of side 16 cm is cut along one diagonal to form two triangles. What is the perimeter of one triangular piece?

(A) 48 cm
(B) 32 + 16√2 cm
(C) 16 + 16√2 cm
(D) 48 + 16√2 cm

Correct Answer: B

Explanation:

Perimeter = 16 + 16 + 16√2 = 32 + 16√2 cm.

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Question (16)

QN0029548

A farmer divides a rectangular field of dimensions 90 m × 60 m into two equal triangular plots by drawing a diagonal. What is the area of each triangular plot?

(A) 1350 m²
(B) 1800 m²
(C) 2400 m²
(D) 2700 m²

Correct Answer: D

Explanation:

Area of rectangle = 90 × 60 = 5400 m². Each triangle = 5400 ÷ 2 = 2700 m².

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Question (17)

QN0029549

A rectangular room has length 8 m and width 6 m. A carpet of area 36 m² is spread on the floor. What fraction of the floor remains uncovered?

(A) 1/4
(B) 1/3
(C) 1/6
(D) 1/2

Correct Answer: A

Explanation:

Area of floor = 8 × 6 = 48 m². Uncovered area = 48 − 36 = 12 m². Fraction = 12/48 = 1/4.

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Question (18)

QN0029550

A regular hexagon is divided into triangles to calculate its area. This method works because

(A) all triangles are congruent.
(B) the sum of the areas of the triangles equals the area of the polygon.
(C) every triangle has the same perimeter.
(D) the diagonals are equal.

Correct Answer: B

Explanation:

Any polygon can be divided into non-overlapping triangles, and the total area equals the sum of the areas of those triangles.

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Question (19)

QN0029551

A rectangular plot has an area of 720 m². If its length is reduced by 20% while the width remains unchanged, the new area will be

(A) 540 m²
(B) 560 m²
(C) 576 m²
(D) 600 m²

Correct Answer: C

Explanation:

New length = 80% of original. New area = 0.8 × 720 = 576 m².

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Question (20)

QN0029552

Which statement correctly explains why perimeter cannot be used to compare the areas of two figures?

(A) Figures with equal perimeter always have equal area.
(B) A figure with greater perimeter always has greater area.
(C) Two figures may have the same perimeter but different areas.
(D) Perimeter and area are measured in the same units.

Correct Answer: C

Explanation:

Area depends on the enclosed surface, whereas perimeter depends only on the boundary length. Hence, equal perimeters can enclose different areas.

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Question (11)

A rhombus has diagonals 24 cm and 18 cm. A parallelogram has the same area and a base of 27 cm. What is the corresponding height of the parallelogram?

Explanation:

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Question (12)

A rectangular sheet measures 40 cm × 25 cm. Four identical right triangles, each of area 25 cm², are cut from its corners. What is the area of the remaining sheet?

Explanation:

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Question (13)

A trapezium has parallel sides in the ratio 3 : 5. If their sum is 64 cm and the height is 10 cm, what is its area?

Explanation:

Link:

Question (14)

A triangle and a parallelogram stand on the same base and have the same height. If the area of the triangle is 54 cm², what is the area of the parallelogram?

Explanation:

Link:

Question (15)

A square of side 16 cm is cut along one diagonal to form two triangles. What is the perimeter of one triangular piece?

Explanation:

Link:

Question (16)

A farmer divides a rectangular field of dimensions 90 m × 60 m into two equal triangular plots by drawing a diagonal. What is the area of each triangular plot?

Explanation:

Link:

Question (17)

A rectangular room has length 8 m and width 6 m. A carpet of area 36 m² is spread on the floor. What fraction of the floor remains uncovered?

Explanation:

Link:

Question (18)

A regular hexagon is divided into triangles to calculate its area. This method works because

Explanation:

Link:

Question (19)

A rectangular plot has an area of 720 m². If its length is reduced by 20% while the width remains unchanged, the new area will be

Explanation:

Link:

Question (20)

Which statement correctly explains why perimeter cannot be used to compare the areas of two figures?

Explanation:

Link:

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