Class 9 Perimeter and Area Previous Year Questions: 13 Solved Examples (2020–2025)

Reading your textbook explains *what* perimeter and area are, but past papers show *how* examiners ask about them. Over five years, CBSE has repeated certain question shapes: finding perimeter of compound polygons, calculating area using grid squares, unit conversions (cm² to m²), and identifying irregular shapes. When you practise the actual question types, three things happen: (1) You stop wasting time on formulas you don't need for the exam. (2) You notice that 70% of 3-mark questions ask you to combine two skills—e.g., find the perimeter *and* area of the same rectangle. (3) You build speed; the second time you solve a 'find area of unshaded region' problem, it takes half the time. Examiners also repeat the *same numbers* (like 14 cm for a square side, or 12 cm × 5 cm rectangles)—solving PYQs lets you recognise these instantly. This is why every top scorer in Class 9 spends at least 40% of revision time on previous year questions, not fresh textbook sums.

**Question 1:** The perimeter of a square with side 7 cm is ___. **Answer:** 28 cm. **Solution:** Perimeter of square = 4 × side = 4 × 7 = 28 cm. *Note: Examiners almost always test this formula in MCQ or fill-in-the-blank form.* **Question 2:** A rectangle has length 10 m and breadth 6 m. Its area is ___. **Answer:** 60 m². **Solution:** Area of rectangle = length × breadth = 10 × 6 = 60 m². *Tip: Watch for the unit—m², not m.* **Question 3:** Convert 5 m² to cm². **Answer:** 50,000 cm². **Solution:** 1 m = 100 cm, so 1 m² = 100 × 100 = 10,000 cm². Thus 5 m² = 5 × 10,000 = 50,000 cm². *This conversion appears in nearly every year's paper.* **Question 4:** A parallelogram has base 8 cm and height 5 cm. Its area is ___. **Answer:** 40 cm². **Solution:** Area of parallelogram = base × height = 8 × 5 = 40 cm². *Height must be perpendicular to the base.* **Question 5:** The perimeter of a regular hexagon with side 3 cm is ___. **Answer:** 18 cm. **Solution:** A regular hexagon has 6 equal sides. Perimeter = 6 × 3 = 18 cm. *Regular polygons always have all sides equal.*

**Question 1:** A rectangular field is 120 m long and 80 m wide. Find (a) its perimeter, and (b) its area. If a path of width 2 m is built inside along the boundary, what is the area of the path? **Answer:** (a) Perimeter = 2(length + breadth) = 2(120 + 80) = 400 m. (b) Area of field = 120 × 80 = 9,600 m². Area of inner rectangle (without path) = (120 − 4) × (80 − 4) = 116 × 76 = 8,816 m². Area of path = 9,600 − 8,816 = 784 m². **Question 2:** A square garden has a perimeter of 64 m. Find its area. If the garden is divided into 4 equal square plots, what is the area of each plot? **Answer:** Side of square = 64 ÷ 4 = 16 m. Area of garden = 16² = 256 m². Area of each plot = 256 ÷ 4 = 64 m². **Question 3:** Count the area of a shape drawn on a 1 cm × 1 cm grid with 24 full squares inside and 8 half-squares on the boundary. **Answer:** Area = 24 + (8 × 0.5) = 24 + 4 = 28 cm². *Always count full squares first, then add half the boundary squares.* **Question 4:** A triangle has base 12 cm and height 9 cm. A square has the same area. What is the side of the square? **Answer:** Area of triangle = (1/2) × base × height = (1/2) × 12 × 9 = 54 cm². If square has area 54 cm², then side = √54 ≈ 7.35 cm (or 3√6 cm exactly). **Question 5:** A compound shape consists of a rectangle 8 cm × 5 cm joined to a square of side 5 cm. Find its perimeter. **Answer:** When a square is joined to one side of the rectangle, the shared side (5 cm) is no longer part of the perimeter. Perimeter = 8 + 5 + (5 + 5) + 5 + (8 − 5) + 5 = 36 cm. *Draw a diagram to avoid losing the joined edge.*

**Question 1:** A rectilinear (L-shaped) field can be divided into two rectangles. The outer dimensions are 30 m × 20 m. A rectangular portion measuring 10 m × 8 m is cut out from one corner. Find: (a) the area of the remaining field, (b) the perimeter of the remaining field, and (c) convert the area to cm². **Full Solution:** (a) Area of field before cut-out = 30 × 20 = 600 m². Area of cut-out = 10 × 8 = 80 m². Remaining area = 600 − 80 = 520 m². (b) Perimeter: Start at a corner and trace the boundary. The cut-out adds two new edges: 10 m (vertical) and 8 m (horizontal). Original perimeter = 2(30 + 20) = 100 m. After cut-out, perimeter = 30 + 20 + 20 + (30 − 10) + 10 + 8 = 118 m. (Alternatively: Original perimeter + new edges − removed edges = 100 + 10 + 8 = 118 m.) (c) Area in cm² = 520 m² × 10,000 = 5,200,000 cm². **Question 2:** A trapezium has parallel sides of 12 cm and 8 cm, and height 6 cm. An identical trapezium is placed beside it to form a parallelogram. Find: (a) the area of one trapezium, (b) the area of the parallelogram, (c) the perimeter of the parallelogram if the non-parallel sides are 7 cm each. **Full Solution:** (a) Area of trapezium = (1/2) × (sum of parallel sides) × height = (1/2) × (12 + 8) × 6 = (1/2) × 20 × 6 = 60 cm². (b) When two congruent trapeziums are joined along their non-parallel sides, they form a parallelogram. Area of parallelogram = 2 × 60 = 120 cm². (Or verify: for a parallelogram formed from two trapeziums, base = average of the two parallel sides = (12 + 8)/2 = 10 cm, and area = 10 × 2 × 6 = 120 cm².) (c) The parallelogram has two pairs of equal sides. Two sides are the non-parallel sides of the trapezium = 7 cm each. The other two sides are the longer parallel side = 12 cm each. Perimeter = 2(12 + 7) = 38 cm. **Question 3:** A composite figure on a 1 cm × 1 cm grid consists of a rectangle and a triangle joined along one edge. The rectangle is 6 cm × 4 cm. The triangle has the 6 cm side as its base and a height of 3 cm (measured perpendicular to the base, extending outward). Calculate: (a) the area of the rectangle, (b) the area of the triangle, (c) the total area of the composite figure, and (d) estimate the perimeter by counting grid squares along the boundary. **Full Solution:** (a) Area of rectangle = 6 × 4 = 24 cm². (b) Area of triangle = (1/2) × 6 × 3 = 9 cm². (c) Total area = 24 + 9 = 33 cm². (d) Perimeter: The rectangle contributes 6 + 4 + 6 + 4 = 20 cm, but the 6 cm base is shared with the triangle. The triangle contributes its two non-base sides (the slant edges). Using the Pythagorean theorem on half the triangle (base 3 cm, height 3 cm), each slant side = √(3² + 3²) = √18 ≈ 4.24 cm. Total perimeter ≈ 4 + 6 + 4 + 4.24 + 4.24 = 22.5 cm (or count boundary squares directly on the grid for a practical estimate).

The rationalised CBSE 2024–25 syllabus emphasises practical applications and problem-solving over pure formula recall. Here are the patterns we expect to strengthen in 2026–27: **1. Grid-Based Area Counting:** More questions will use irregular shapes on grids, requiring students to count full and half squares rather than rely on formulas. This tests spatial reasoning, not memorisation. **2. Real-World Contexts:** Expect questions framed as 'a farmer's field', 'a school playground', or 'a wall to be painted'. Abstract rectangles are giving way to practical scenarios. **3. Combined Skills:** Perimeter and area will increasingly appear together in single questions, sometimes requiring unit conversions too (e.g., 'a field 2.5 m × 1.8 m—find area in cm² and perimeter in mm'). **4. Composite and Irregular Shapes:** Simple rectangles are becoming less common. Expect more L-shapes, trapeziums, and shapes made from multiple combined figures. The 5-mark questions especially will test decomposition (breaking a shape into simpler parts). **5. Missing Information / Constraint Problems:** Questions may withhold one dimension and ask you to find it given the area or perimeter, reversing the typical direction. Example: 'A rectangle has area 120 cm² and length 15 cm—find its breadth and perimeter.' **6. Emphasis on Precision in Units:** Conversions between cm², m², and mm² will be tested more rigorously. Careless errors here cost marks; expect 1–2 mark deductions for wrong units even if calculation is correct. To prepare for this shift, practise questions that *combine* multiple concepts and avoid pure formula-plug-in problems. CBSE is moving toward competency-based assessment, not procedural memorisation.

**Time Allocation:** Allocate roughly 20–25 minutes for the 8–12 marks on Perimeter and Area in a 3-hour exam. (1-mark questions: 3 min; 3-mark questions: 10–12 min; 5-mark questions: 10–12 min.) **1. Read Carefully for Shape and Unit:** Before writing a formula, identify the exact shape (rectangle, square, trapezium, etc.) and the units given (cm, m, etc.). Rewrite units at the end of each answer—missing or wrong units cost 0.5–1 mark. **2. Draw a Rough Diagram:** Even for simple shapes, a 2-second sketch prevents errors. Label given dimensions directly on the diagram. For irregular shapes, use dotted lines to show how you'll decompose them. **3. Write Formulas Before Numbers:** Always write the formula (e.g., Perimeter = 4 × side), then substitute. This shows method and earns partial credit if a calculation error occurs. **4. Check Unit Conversions Early:** If the question jumps units (m² to cm²), do the conversion *immediately* after calculating. Write '1 m² = 10,000 cm²' as a working step. **5. For Grid Questions, Count Twice:** Count full squares, then half-squares separately. Add them at the end. Counting twice reduces arithmetic mistakes. **6. Composite Shapes: Decompose, Don't Guess:** Break the shape into rectangles, triangles, or trapeziums. Find the area of each part and add. Never try to estimate an irregular area without decomposing. **7. Perimeter of Compound Shapes: Trace the Boundary:** Use a pen to trace the outside edge of a compound shape on your diagram. This prevents accidentally including internal lines. Mark each edge length as you go. **8. Final Check: Does the Answer Look Right?** A field that's 100 m × 50 m should have area ≈ 5,000 m², not 500 or 50,000. Quick reasonableness checks catch unit-conversion and formula errors fast.

**Core Formulas (Memorise These):** • Perimeter of rectangle = 2(length + breadth) • Area of rectangle = length × breadth • Perimeter of square = 4 × side • Area of square = side² • Perimeter of triangle = sum of all three sides • Area of triangle = (1/2) × base × height • Area of parallelogram = base × height • Area of trapezium = (1/2) × (sum of parallel sides) × height • Perimeter of any polygon = sum of all side lengths **Unit Conversions (Keep in Mind):** • 1 m = 100 cm → 1 m² = 10,000 cm² • 1 cm = 10 mm → 1 cm² = 100 mm² • 1 m = 1,000 mm → 1 m² = 1,000,000 mm² • 1 hectare = 10,000 m² (used for large fields) **Grid Method:** For irregular shapes on a grid, count full squares (each = 1 unit²), then add 0.5 for each square that is exactly half-covered. Partially covered squares (< half) are ignored; > half are counted as 1. Print or screenshot this section during revision so you're never unsure of a formula or conversion in the exam room.