Mensuration of 2D Shapes - Exam Prep Questions

Mensuration of 2D Shapes - Proof-based Questions - Case Studies

Q. A rectangle has a length of 8 cm and a width of 3 cm. What is its perimeter?

A. 22 cm
B. 24 cm
C. 20 cm
D. 26 cm

Solution

Perimeter = 2(length + width) = 2(8 + 3) = 22 cm.

Correct Answer: A — 22 cm

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Q. A trapezoid has bases of lengths 10 cm and 6 cm, and a height of 4 cm. What is its area?

A. 32 cm²
B. 40 cm²
C. 24 cm²
D. 28 cm²

Solution

Area = 1/2 * (base1 + base2) * height = 1/2 * (10 + 6) * 4 = 32 cm².

Correct Answer: A — 32 cm²

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Q. If a square has a perimeter of 32 cm, what is the area of the square?

A. 64 cm²
B. 128 cm²
C. 16 cm²
D. 32 cm²

Solution

Side length = perimeter/4 = 32/4 = 8 cm. Area = side² = 8² = 64 cm².

Correct Answer: A — 64 cm²

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Q. If a square has a perimeter of 40 cm, what is the area of the square?

A. 100 cm²
B. 160 cm²
C. 200 cm²
D. 250 cm²

Solution

Side length = perimeter/4 = 40/4 = 10 cm. Area = side² = 10² = 100 cm².

Correct Answer: A — 100 cm²

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Q. If two angles of a triangle are 45° and 55°, what is the measure of the third angle?

A. 80°
B. 90°
C. 100°
D. 70°

Solution

Sum of angles in a triangle = 180°. Third angle = 180° - (45° + 55°) = 80°.

Correct Answer: A — 80°

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Q. Two triangles are similar with a ratio of their corresponding sides as 3:5. If the area of the smaller triangle is 27 cm², what is the area of the larger triangle?

A. 45 cm²
B. 75 cm²
C. 60 cm²
D. 50 cm²

Solution

Area ratio = (side ratio)² = (3/5)² = 9/25. Let area of larger triangle be A. 27/A = 9/25, A = 27 * (25/9) = 75 cm².

Correct Answer: B — 75 cm²

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Q. Two triangles are similar. If the sides of the first triangle are 3 cm, 4 cm, and 5 cm, what is the area of the second triangle if its longest side is 10 cm?

A. 40 cm²
B. 20 cm²
C. 30 cm²
D. 50 cm²

Solution

The ratio of the sides is 10/5 = 2. Area ratio = (2)² = 4. Area of first triangle = 6 cm². Area of second triangle = 6 * 4 = 24 cm².

Correct Answer: B — 20 cm²

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Q. What is the circumference of a circle with a radius of 3 cm?

A. 6π cm
B. 9π cm
C. 12π cm
D. 15π cm

Solution

Circumference = 2πr = 2π(3) = 6π cm.

Correct Answer: A — 6π cm

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Q. What is the circumference of a circle with a radius of 5 cm?

A. 10π cm
B. 15π cm
C. 20π cm
D. 25π cm

Solution

Circumference = 2πr = 2π(5) = 10π cm.

Correct Answer: A — 10π cm

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Mensuration of 2D Shapes - Proof-based Questions - Case Studies

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