Class 7 Area of Paths and Borders — practice questions with answers
Perimeter and Area · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. A path runs around the outside of a rectangular lawn. How do you find the area of the path?
AOuter area − lawn area
BPath width × lawn area
COuter perimeter − lawn perimeter
DOuter area + lawn area
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Answer: A) Outer area − lawn area
The big rectangle (lawn + path) minus the lawn leaves only the path. So area of path = outer area − inner area.
2. A drawing sheet is 30 cm by 20 cm. Ananya leaves a 2 cm margin on every side. What area is left for her drawing?
A504 cm²
B600 cm²
C184 cm²
D416 cm²
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Answer: D) 416 cm²
Drawing area: (30 − 4) × (20 − 4) = 26 × 16 = 416 cm². (504 cm² subtracts 2 cm only once from each side.)
3. A swimming pool is 25 m by 10 m. A tiled border 1.5 m wide is laid around it on the outside, at ₹80 per m². Find the cost of tiling.
A₹29,120
B₹9,120
C₹8,400
D₹4,560
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Answer: B) ₹9,120
Outer: (25 + 3) × (10 + 3) = 28 × 13 = 364 m². Border = 364 − 250 = 114 m². Cost = 114 × 80 = ₹9,120. (₹8,400 uses 2 × (25 + 10) × 1.5 = 105 m² and misses the corners.)
4. Neha uses 2 × (12 + 8) × 1 = 40 m² for a 1 m path along the INSIDE of a 12 m × 8 m yard. What correction does she need?
AAdd 4 m²: 44 m²
BSubtract 8 m²: 32 m²
CSubtract 4 m²: 36 m²
DNone: 40 m²
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Answer: C) Subtract 4 m²: 36 m²
Inside, the long strips and short strips overlap at the 4 corners, so 4 m² is counted twice. Correct: 96 − 10 × 6 = 36 m².
5. A lawn 30 m by 20 m has a 2 m path around its outside and a circular flower bed of radius 7 m inside it. What is the total area of the path and the flower bed? (Use π=722)
A216 m²
B370 m²
C154 m²
D446 m²
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Answer: B) 370 m²
Path: 34 × 24 − 600 = 816 − 600 = 216 m². Bed: 722×7×7=154 m². Total = 216 + 154 = 370 m².