Class 9 Rectangle, Rhombus and Square — practice questions with answers
Geometry — Quadrilaterals · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. The diagonals of a rectangle are always:
Aunequal but bisect each other
Bequal and bisect each other
Cperpendicular to each other
Dequal to the sides
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Answer: B) equal and bisect each other
A rectangle is a parallelogram, so its diagonals bisect each other; because all angles are 90°, they are also equal. They are perpendicular only when the rectangle is a square.
2. What is the length of the diagonal of a square of side 5 cm?
A10 cm
B5√2 cm
C5 cm
D25 cm
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Answer: B) 5√2 cm
Diagonal² = 5² + 5² = 50, so diagonal = √50 = 5√2 cm (about 7.07 cm). 10 cm just doubles the side.
3. A rectangle has a diagonal of 10 cm and one side of 6 cm. What is its area?
A80 cm²
B24 cm²
C48 cm²
D60 cm²
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Answer: C) 48 cm²
Other side = √(10² − 6²) = √64 = 8 cm. Area = 6 × 8 = 48 cm². (60 cm² multiplies the diagonal by a side.)
4. A square rangoli has a diagonal of 3 m. What is its area?
A3 m²
B9 m²
C4.5 m²
D6 m²
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Answer: C) 4.5 m²
A square is a rhombus, so area = ½ × d × d = ½ × 3 × 3 = 4.5 m². (9 m² treats the diagonal as a side.)
5. Square ABCD has an equilateral triangle BCE drawn outside it on side BC. Find ∠AEB.
A30°
B45°
C75°
D15°
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Answer: D) 15°
AB = BC = BE, so △ABE is isosceles. ∠ABE = 90° + 60° = 150°, so ∠AEB = (180° − 150°) ÷ 2 = 15°.