Major Competitive Exams

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Q. If the area of a rectangle is calculated as 50 m² with a length of 10 m and an uncertainty of ±0.1 m in length, what is the uncertainty in the area?

A. 1 m²
B. 0.5 m²
C. 0.2 m²
D. 0.1 m²

Solution

Uncertainty in area = 2 * length * uncertainty in length = 2 * 10 * 0.1 = 2 m².

Correct Answer: B — 0.5 m²

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Q. If the area of a rhombus is 72 cm² and one diagonal is 12 cm, what is the length of the other diagonal?

A. 12 cm
B. 18 cm
C. 24 cm
D. 30 cm

Solution

Area = (d1 × d2) / 2. 72 = (12 × d2) / 2, so d2 = 12 cm.

Correct Answer: B — 18 cm

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Q. If the area of a rhombus is 72 square cm and one diagonal is 12 cm, what is the length of the other diagonal?

A. 12 cm
B. 18 cm
C. 24 cm
D. 6 cm

Solution

Area = (1/2) × d1 × d2. Thus, 72 = (1/2) × 12 × d2, giving d2 = 12 cm.

Correct Answer: B — 18 cm

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Q. If the area of a sector of a circle is 25π cm² and the radius is 10 cm, what is the angle of the sector in degrees?

A. 90 degrees
B. 60 degrees
C. 45 degrees
D. 30 degrees

Solution

Area of a sector = (θ/360) × πr². Thus, 25π = (θ/360) × π(10)². Solving gives θ = 90 degrees.

Correct Answer: A — 90 degrees

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Q. If the area of a sector of a circle is 25π square units and the radius is 5 units, what is the angle of the sector in degrees?

A. 90°
B. 60°
C. 45°
D. 30°

Solution

Area of a sector = (θ/360) × πr². Thus, 25π = (θ/360) × π(5)². Solving gives θ = 90°.

Correct Answer: A — 90°

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Q. If the area of a sector of a circle is 30 cm² and the radius is 5 cm, what is the angle of the sector in degrees?

A. 60°
B. 72°
C. 90°
D. 120°

Solution

Area of a sector = (θ/360) × πr². Thus, 30 = (θ/360) × π × 25. Solving gives θ = (30 × 360)/(25π) ≈ 72°.

Correct Answer: B — 72°

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Q. If the area of a square is 64 cm², what is the length of one side? (2022)

A. 6 cm
B. 7 cm
C. 8 cm
D. 9 cm

Solution

Area of a square = side². Therefore, side = √64 = 8 cm.

Correct Answer: C — 8 cm

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Q. If the area of a square is 64 square meters, what is the length of one side?

A. 6 meters
B. 8 meters
C. 10 meters
D. 12 meters

Solution

Area = side². Thus, 64 = side², giving side = √64 = 8 meters.

Correct Answer: B — 8 meters

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Q. If the area of a square is 64 square units, what is the length of one side?

A. 6 units
B. 8 units
C. 10 units
D. 12 units

Solution

Area = side². Thus, side = √64 = 8 units.

Correct Answer: B — 8 units

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Q. If the area of a trapezium is 60 cm² and the lengths of the two parallel sides are 10 cm and 14 cm, what is the height?

A. 4 cm
B. 5 cm
C. 6 cm
D. 7 cm

Solution

Area = (1/2) × (a + b) × height. 60 = (1/2) × (10 + 14) × height. Solving gives height = 5 cm.

Correct Answer: B — 5 cm

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Q. If the area of a trapezium is 60 square units and the lengths of the parallel sides are 10 units and 20 units, what is the height?

A. 4 units
B. 6 units
C. 8 units
D. 10 units

Solution

Area = (1/2) × (base1 + base2) × height. Thus, 60 = (1/2) × (10 + 20) × height, giving height = 60 / 15 = 4 units.

Correct Answer: B — 6 units

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Q. If the area of a trapezium is 60 square units and the lengths of the two parallel sides are 10 units and 20 units, what is the height?

A. 4 units
B. 6 units
C. 5 units
D. 8 units

Solution

Area = (1/2) × (base1 + base2) × height. Thus, 60 = (1/2) × (10 + 20) × height, giving height = 60 / 15 = 4 units.

Correct Answer: B — 6 units

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Q. If the area of a triangle is 24 cm² and the base is 8 cm, what is the height?

A. 6 cm
B. 8 cm
C. 12 cm
D. 3 cm

Solution

Area = 1/2 * base * height. Therefore, 24 = 1/2 * 8 * height, which gives height = 6 cm.

Correct Answer: A — 6 cm

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Q. If the area of a triangle is 24 cm² and the height is 6 cm, what is the base?

A. 4 cm
B. 6 cm
C. 8 cm
D. 10 cm

Solution

Area = (base × height) / 2, so base = (2 × Area) / height = (2 × 24 cm²) / 6 cm = 8 cm.

Correct Answer: C — 8 cm

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Q. If the area of a triangle is 24 square cm and the base is 8 cm, what is the height?

A. 3 cm
B. 6 cm
C. 8 cm
D. 12 cm

Solution

The area of a triangle is given by the formula Area = 1/2 * base * height. Thus, 24 = 1/2 * 8 * height, which gives height = 6 cm.

Correct Answer: B — 6 cm

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Q. If the area of a triangle is 30 cm² and the base is 10 cm, what is the height? (2020)

A. 3 cm
B. 6 cm
C. 9 cm
D. 12 cm

Solution

Area = 1/2 * base * height. Thus, 30 = 1/2 * 10 * height. Solving gives height = 6 cm.

Correct Answer: B — 6 cm

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Q. If the area of a triangle is 30 square units and the base is 10 units, what is the height?

A. 3
B. 5
C. 6
D. 10

Solution

Area = 1/2 * base * height => height = 30/(1/2 * 10) = 6.

Correct Answer: B — 5

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Q. If the area of a triangle is 48 cm² and the base is 12 cm, what is the height? (2022)

A. 6 cm
B. 8 cm
C. 4 cm
D. 10 cm

Solution

Area = 1/2 * base * height, so 48 = 1/2 * 12 * height, height = 48/(6) = 8 cm.

Correct Answer: B — 8 cm

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Q. If the area of a triangle is 50 cm² and the height is 10 cm, what is the base?

A. 5 cm
B. 10 cm
C. 15 cm
D. 20 cm

Solution

Area = (base × height) / 2, so base = (2 × Area) / height = (2 × 50 cm²) / 10 cm = 10 cm.

Correct Answer: D — 20 cm

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Q. If the area of a triangle is 50 square cm and its base is 10 cm, what is the height of the triangle?

A. 5 cm
B. 10 cm
C. 15 cm
D. 20 cm

Solution

Area of a triangle = (1/2) × base × height. Thus, 50 = (1/2) × 10 × height. Solving gives height = 10 cm.

Correct Answer: A — 5 cm

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Q. If the area of a triangle is 50 square units and its base is 10 units, what is the height of the triangle?

A. 5 units
B. 10 units
C. 15 units
D. 20 units

Solution

Area of a triangle = (1/2) × base × height. Thus, 50 = (1/2) × 10 × height. Solving gives height = 10 units.

Correct Answer: A — 5 units

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Q. If the area of a triangle is 60 square units and the base is 10 units, what is the height? (2019)

A. 12
B. 10
C. 8
D. 6

Solution

The area of a triangle is given by (1/2) * base * height. Thus, 60 = (1/2) * 10 * height. Solving for height gives height = 12 units.

Correct Answer: A — 12

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Q. If the area of a triangle is given by the formula A = 1/2 * base * height, what is the area of a triangle with a base of 10 cm and a height of 5 cm?

A. 25 cm²
B. 50 cm²
C. 15 cm²
D. 30 cm²

Solution

Substituting the values into the area formula: A = 1/2 * 10 * 5 = 25 cm².

Correct Answer: A — 25 cm²

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Q. If the area of triangle ABC is 30 cm² and the base BC = 10 cm, what is the height from A to BC?

A. 5 cm
B. 6 cm
C. 7 cm
D. 8 cm

Solution

Area = 1/2 * base * height. Therefore, 30 = 1/2 * 10 * height, height = 6 cm.

Correct Answer: B — 6 cm

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Q. If the area of triangle ABC is 30 square units and the base BC = 10 units, what is the height from A to BC?

A. 5
B. 6
C. 7
D. 8

Solution

Area = 1/2 * base * height => 30 = 1/2 * 10 * height => height = 30 / 5 = 6.

Correct Answer: A — 5

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Q. If the area of triangle ABC is 30 square units and the base BC is 10 units, what is the height from A to BC?

A. 3
B. 5
C. 6
D. 7

Solution

Area = 1/2 * base * height. Thus, 30 = 1/2 * 10 * height. Height = 6.

Correct Answer: B — 5

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Q. If the area of triangle ABC is 60 cm² and the base BC = 12 cm, what is the height from A to BC?

A. 5 cm
B. 10 cm
C. 12 cm
D. 15 cm

Solution

Area = (1/2) * base * height. Therefore, 60 = (1/2) * 12 * height, height = 10 cm.

Correct Answer: B — 10 cm

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Q. If the area of triangle ABC is 60 square units and the base AC is 12 units, what is the height from point B to line AC? (2019)

A. 5 units
B. 10 units
C. 15 units
D. 20 units

Solution

Area = 1/2 * base * height. Therefore, 60 = 1/2 * 12 * height, which gives height = 10 units.

Correct Answer: A — 5 units

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Q. If the area of triangle ABC is 60 square units and the base is 10 units, what is the height of the triangle? (2019)

A. 6 units
B. 12 units
C. 10 units
D. 8 units

Solution

Area = 1/2 * base * height. Therefore, 60 = 1/2 * 10 * height, which gives height = 12 units.

Correct Answer: A — 6 units

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Q. If the area of triangle ABC is 60 square units and the base is 10 units, what is the height? (2019)

A. 6 units
B. 12 units
C. 10 units
D. 8 units

Solution

Area = 1/2 * base * height. Therefore, 60 = 1/2 * 10 * height, which gives height = 12 units.

Correct Answer: A — 6 units

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Major Competitive Exams

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