Practice Questions
Concept Explanation
Area measures the region enclosed by a 2D figure (square units). Combine standard formulas and decomposition (subtract overlaps, split into triangles/rectangles).
Quick Reference
- Triangle: ½ × b × h
- Rectangle: l × b; Circle: πr² (π = 22/7)
- Path around rectangle: outer area − inner area
- Shaded region = total − unshaded parts
Example
Square 10 cm with corner circles of radius 1 cm removed (conceptually): subtract four quarter circles = one full circle πr².
Common Trap
Convert units before calculating (cm vs m). For composite figures, draw and label all regions.
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Q1 EasyRectangle 20 m × 15 m. Area:Explanation20 × 15 = 300 sq m. Hence the answer is 300 sq m.
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Q2 EasyCircle r = 7 cm (π = 22/7). Area:ExplanationArea = 154 sq cm. Hence the answer is 154 sq cm.
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Q3 EasyArea of triangle with sides 6, 8, 10 cm is:ExplanationRight triangle: area = ½ × 6 × 8 = 24 sq cm. Hence the answer is 24 sq cm.
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Q4 EasyTriangle base 12 cm, height 9 cm. Area:Explanation½ × 12 × 9 = 54 sq cm. Hence the answer is 54 sq cm.
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Q5 EasyA square of side 14 cm has four equal semicircles drawn on its sides (inward). Area of square is:ExplanationArea of square = 14² = 196 sq cm (question asks square area). Hence the answer is 196 sq cm.
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Q6 EasyParallelogram base 16 cm, height 7 cm. Area:Explanation16 × 7 = 112 sq cm. Hence the answer is 112 sq cm.
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Q7 EasyRhombus diagonals 8 and 6 cm. Area:Explanation½ × 8 × 6 = 24 sq cm. Hence the answer is 24 sq cm.
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Q8 MediumA rectangular field 40 m × 30 m has a path 2 m wide inside along the boundary. Area of the path is:ExplanationOuter = 1200 sq m. Inner = 36 × 26 = 936 sq m. Path = 1200 − 936 = 264 sq m. Hence the answer is 264 sq m.
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Q9 MediumHall 12 m × 10 m, carpet leaves 1 m border. Carpet area:ExplanationInner 10 × 8 = 80 sq m. Hence the answer is 80 sq m.
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Q10 MediumTwo concentric circles r = 3 and 5 cm (π = 22/7). Ring area:ExplanationRing area = π(R² − r²) = (22/7) × (25 − 9) = (22/7) × 16 = 352/7 sq cm ≈ 50.29 sq cm. Hence the answer is 50 sq cm.
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Q11 MediumL-shaped floor: 8 m × 6 m rectangle with 3 m × 2 m corner cut. Area is:ExplanationArea = 48 − 6 = 42 sq m. Hence the answer is 42 sq m.
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Q12 MediumEquilateral triangle side 4 cm. Area is:ExplanationArea = (√3/4) × 16 = 4√3 sq cm. Hence the answer is 4√3 sq cm.
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Q13 HardSquare and circle have same perimeter 44 cm (π = 22/7). Circle area:ExplanationCircle C = 44, r = 7, area = 154 sq cm. Hence the answer is 154 sq cm.
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Q14 HardRadius of circle is 7 cm (π = 22/7). Area of square inscribed in the circle is:ExplanationDiagonal of square = diameter = 14. If side s, s√2 = 14, s² = 196/2 = 98 sq cm. Hence the answer is 98 sq cm.
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DS1 Easy
What is the area of the rectangular field?
Statement ILength is 40 m and breadth is 30 m.
Statement IIPerimeter is 140 m and length exceeds breadth by 10 m.
ExplanationStatement I alone: 40 × 30 = 1200 sq m. Statement II alone: solves l = 40, b = 30. Both work but I alone is direct. Answer: A. -
DS2 Easy
What is the area of the triangle?
Statement IIt is a right triangle with legs 9 cm and 12 cm.
Statement IIHypotenuse is 15 cm and one leg is 9 cm.
ExplanationEach gives legs 9 and 12, area = 54 sq cm. Answer: D.
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DS3 Medium
What is the area of the path around the inner rectangle?
Statement IOuter rectangle is 20 m × 14 m.
Statement IIPath width is 1 m on all sides inside.
ExplanationNeed outer dimensions and path width: inner 18 × 12, path = 280 − 216 = 64 sq m. Answer: C. -
DS4 Hard
What is the shaded area? (π = 22/7)
Statement ISquare side is 14 cm.
Statement IIFour quarter circles of radius 7 cm are removed from the square corners.
ExplanationNeed both: square 196, four quarters = one circle 154, shaded = 42 sq cm. Answer: C.