Practice Questions
Concept Explanation
A quadrilateral is a four-sided polygon. Sum of interior angles = 360°. Common types: square, rectangle, parallelogram, rhombus, trapezium, kite.
Area Formulas
- Square: side²; perimeter = 4 × side
- Rectangle: length × breadth
- Parallelogram: base × height (perpendicular height)
- Rhombus: ½ × d1 × d2
- Trapezium: ½ × (sum of parallel sides) × height
Example
Rhombus with diagonals 12 cm and 16 cm: area = ½ × 12 × 16 = 96 sq cm.
Common Trap
Slant side of a parallelogram is not the height unless it is perpendicular to the base.
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Q1 EasyArea of a square with side 8 cm is:ExplanationArea of square = side² = 8² = 64 sq cm. Hence the answer is 64 sq cm.
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Q2 EasyPerimeter of square side 8 cm is:ExplanationPerimeter = 4 × 8 = 32 cm. Hence the answer is 32 cm.
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Q3 EasyArea of a rectangle 12 cm × 5 cm is:ExplanationArea = length × breadth = 12 × 5 = 60 sq cm. Hence the answer is 60 sq cm.
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Q4 EasyArea of a parallelogram with base 10 cm and height 6 cm is:ExplanationArea = base × height = 10 × 6 = 60 sq cm. Hence the answer is 60 sq cm.
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Q5 EasyParallelogram base 15 cm, height 4 cm. Area:ExplanationArea = 15 × 4 = 60 sq cm. Hence the answer is 60 sq cm.
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Q6 EasySum of interior angles of any quadrilateral is:ExplanationInterior angle sum of n-gon = (n − 2) × 180°; for n = 4, sum = 360°. Hence the answer is 360°.
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Q7 EasyRectangle area 48 sq cm, length 8 cm. Breadth is:ExplanationBreadth = area / length = 48 / 8 = 6 cm. Hence the answer is 6 cm.
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Q8 EasyPerimeter of a rectangle 12 cm × 5 cm is:ExplanationPerimeter = 2(12 + 5) = 2 × 17 = 34 cm. Hence the answer is 34 cm.
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Q9 MediumSquare diagonal 10√2 cm. Side is:ExplanationDiagonal = side × √2, so side = 10√2 / √2 = 10 cm. Hence the answer is 10 cm.
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Q10 MediumA trapezium has parallel sides 8 cm and 12 cm, height 5 cm. Area is:ExplanationArea = ½ × (8 + 12) × 5 = ½ × 20 × 5 = 50 sq cm. Hence the answer is 50 sq cm.
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Q11 MediumTrapezium parallel sides 10 and 14 cm, height 6 cm. Area:ExplanationArea = ½ × (10 + 14) × 6 = 72 sq cm. Hence the answer is 72 sq cm.
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Q12 MediumA rhombus has diagonals 12 cm and 16 cm. Its area is:ExplanationArea = ½ × d1 × d2 = ½ × 12 × 16 = 96 sq cm. Hence the answer is 96 sq cm.
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Q13 MediumSquare area 81 sq cm. Perimeter is:ExplanationSide = √81 = 9 cm. Perimeter = 4 × 9 = 36 cm. Hence the answer is 36 cm.
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Q14 HardRhombus side 5 cm, one diagonal 6 cm. Other diagonal is:ExplanationHalf diagonals 3 and d/2: 5² = 3² + (d/2)², so d = 8 cm. Hence the answer is 8 cm.
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DS1 Easy
What is the area of the rectangle?
Statement ILength is 12 cm.
Statement IIBreadth is 5 cm.
ExplanationNeed both: area = 12 × 5 = 60 sq cm. Answer: C. -
DS2 Easy
What is the perimeter of the square?
Statement IArea is 64 sq cm.
Statement IIDiagonal is 8√2 cm.
ExplanationStatement I: side = 8 cm, perimeter = 32 cm. Statement II: side = 8 cm, perimeter = 32 cm. Each alone sufficient. Answer: D.
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DS3 Medium
What is the area of the rhombus?
Statement IDiagonals are 10 cm and 24 cm.
Statement IIOne diagonal is twice the other.
ExplanationStatement I alone: area = ½ × 10 × 24 = 120 sq cm. Statement II alone does not give numeric diagonals. Answer: A. -
DS4 Medium
What is the area of the trapezium?
Statement IParallel sides are 9 cm and 11 cm.
Statement IIHeight is 5 cm.
ExplanationNeed parallel sides and height: area = ½ × 20 × 5 = 50 sq cm. Answer: C.