Constructions

Q. A right triangle has legs of lengths 6 cm and 8 cm. What is the length of the hypotenuse?

Solution

Hypotenuse = √(6² + 8²) = √(36 + 64) = √100 = 10 cm.

Correct Answer: A — 10 cm

Q. A square has a perimeter of 64 cm. What is the length of one side?

Solution

Perimeter = 4 × side; 64 = 4 × side; side = 64 / 4 = 16 cm.

Correct Answer: A — 16 cm

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

Solution

Area = (1/2) × (base1 + base2) × height = (1/2) × (10 + 6) × 4 = 32 m².

Correct Answer: A — 32 m²

Q. If the length of a rectangle is doubled and the width is halved, how does the area change?

Solution

New area = (2L) × (W/2) = L × W = original area; area doubles.

Correct Answer: B — It doubles

Q. What is the area of a parallelogram with a base of 12 cm and a height of 7 cm?

Solution

Area = base × height = 12 × 7 = 84 cm².

Correct Answer: B — 72 cm²

Q. What is the volume of a cube with a side length of 3 cm?

Solution

Volume = side³ = 3³ = 27 cm³.

Correct Answer: B — 27 cm³

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