Practice Questions
Concept Explanation
Area measures the region enclosed by a 2D figure, in sq cm or sq m.
Quick Reference
- Triangle: ½ × base × height
- Rectangle: length × breadth
- Parallelogram: base × height
- Trapezium: ½ × (a + b) × h
- Circle: πr²
- Rhombus: ½ × d1 × d2
Composite Figures
Split into basic shapes, find each area, then add or subtract as needed.
Example
L-shaped floor: divide into two rectangles and add their areas.
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Q1 Easy
A triangle has base 16 cm and height 9 cm. Area is:
ExplanationArea = ½ × 16 × 9 = 72 sq cm. -
Q2 Easy
A rectangular field is 40 m × 25 m. Area is:
ExplanationArea = 40 × 25 = 1000 sq m. -
Q3 Easy
A circle has radius 10 cm, π = 3.14. Area is:
ExplanationArea = 3.14 × 100 = 314 sq cm. -
Q4 Medium
A trapezium has parallel sides 10 cm and 14 cm, height 6 cm. Area is:
ExplanationArea = ½ × 24 × 6 = 72 sq cm. -
Q5 Medium
A rhombus has diagonals 8 cm and 15 cm. Area is:
ExplanationArea = ½ × 8 × 15 = 60 sq cm. -
Q6 Medium
A square of side 12 cm and a triangle (base 12 cm, height 5 cm) on the same base. Combined area is:
ExplanationSquare 144 + triangle 30 = 174 sq cm. -
Q7 Hard
A room 8 m × 6 m has a circular rug of radius 1 m (π = 3.14). Uncovered floor area is:
ExplanationRoom = 48 sq m. Rug = 3.14 sq m. Uncovered = 44.86 sq m.
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Q8 Medium
A parallelogram has base 10 cm and height 12 cm. Area is:
ExplanationArea = 10 × 12 = 120 sq cm. -
Q9 Hard
An equilateral triangle of side 8 cm has area (√3 ≈ 1.73):
ExplanationArea = (√3/4) × 64 ≈ 27.68 sq cm. -
Q10 Hard
A square is inscribed in a circle of radius 7 cm (π = 22/7). Area outside the square but inside the circle is:
ExplanationCircle = 154 sq cm. Square area = 98 sq cm. Difference = 56 sq cm. -
Q11 Hard
A path 2 m wide runs outside a rectangular lawn 20 m × 14 m. Area of the path is:
ExplanationOuter rectangle 24 × 18 = 432. Inner = 280. Path = 152 sq m. -
Q12 Easy
Cost of painting a wall 12 m × 4 m at Rs. 25 per sq m is:
ExplanationArea = 48 sq m. Cost = 48 × 25 = Rs. 1200. -
Q13 Medium
A triangle and rectangle share base 10 cm. Triangle height 6 cm, rectangle height 8 cm. Total area is:
ExplanationTriangle 30 + rectangle 80 = 110 sq cm. -
Q14 Easy
Diameter of a circle is 20 cm, π = 3.14. Area is:
Explanationr = 10 cm. Area = 3.14 × 100 = 314 sq cm.
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DS1 Easy
What is the area of the triangle?
Statement IBase is 18 cm.
Statement IIHeight is 6 cm.
ExplanationNeed both: area = ½ × 18 × 6 = 54 sq cm. -
DS2 Easy
What is the area of the rectangular field?
Statement ILength is 30 m.
Statement IIBreadth is 18 m.
ExplanationNeed both: area = 540 sq m.
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DS3 Medium
What is the area of the circle? (π = 22/7)
Statement IRadius is 14 cm.
Statement IICircumference is 88 cm.
ExplanationEach alone gives area = 616 sq cm. -
DS4 Medium
What is the combined area of square and triangle on the same base?
Statement ISquare side is 10 cm.
Statement IITriangle base 10 cm and height 4 cm.
ExplanationNeed both: 100 + 20 = 120 sq cm.