1. Find the area of a triangle with base 8 cm and height 6 cm (in cm²).
- A24
- B48
- C14
- D28
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Answer: A) 24
A = × 8 × 6 = 24.
Class 7 Perimeter and Area — 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.
2. A square garden has side 25 m. A circular pond of radius 7 m is dug inside it. Find the area of the garden left around the pond. Use π = (answer in m²).
- A471
- B942
- C516
- D426
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Answer: A) 471
Garden area = 25² = 625 m². Pond area = × 7² = 154 m². Remaining = 625 − 154 = 471 m².
3. The base of a triangle is 18 cm and its area is 90 cm². Find the corresponding height (in cm).
- A11
- B20
- C9
- D10
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Answer: D) 10
A = × b × h → 90 = × 18 × h → 90 = 9h → h = 10 cm.
4. A window is a rectangle 2 m wide and 1.5 m tall with a semicircle on top whose diameter is the 2 m width. Find the total area of glass in the window. Use π = 3.14 (answer in m², to 2 decimal places).
- A6.14
- B9.28
- C4.57
- D3.00
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Answer: C) 4.57
Rectangle = 2 × 1.5 = 3 m². The semicircle has diameter 2 m, so radius 1 m, and area = × 3.14 × 1² = 1.57 m². Total = 3 + 1.57 = 4.57 m². Forgetting to halve the circle gives 6.14; using 2 m as the radius gives 9.28.
5. A rectangular park is 60 m by 40 m. Two paths, each 3 m wide, run through the middle and cross each other — one parallel to the length and one parallel to the breadth. Find the total area of the two paths (in m²).
- A291
- B300
- C309
- D180
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Answer: A) 291
Path along the length = 60 × 3 = 180 m²; path along the breadth = 40 × 3 = 120 m². Where they cross, a 3 m × 3 m square (9 m²) has been counted twice, so subtract it once: 180 + 120 − 9 = 291 m². Forgetting the overlap gives the trap 300 m²; adding it gives 309 m².
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