**Perimeter Formulas**
**Rectangle:** P = 2 × (length + breadth) or P = 2(l + b)
**Square:** P = 4 × side or P = 4s
**Triangle:** P = side₁ + side₂ + side₃
**Regular Polygon:** P = number of sides × length of one side
**Key Definition**
Perimeter = total distance along the outer boundary of a closed shape. Always measured in linear units (cm, m, km).
**Why These Formulas Work**
A rectangle has opposite sides equal (length appears twice, breadth appears twice). A square has all four sides equal, so we multiply one side by 4. A triangle has three sides we simply add.
**Real-Life Steps**
1. Identify the shape
2. Measure or note all side lengths in same units
3. Apply correct formula or add all sides
4. Write answer with units (cm, m, etc.)
**Don't Confuse:** Perimeter (boundary distance) ≠ Area (space covered inside). Perimeter uses addition; area uses multiplication of two measurements.
**Diagrams to Remember:** Rectangle with length and breadth marked; square with all sides equal; triangle with three sides labeled.
**Common Exam Tricks:** Questions often mix perimeter with multiple rounds or need you to find missing side given perimeter.
Q1. The perimeter of a shape is the total __________ around its boundary.
Answer: A — Perimeter is defined as the total distance measured along the outer boundary of a closed shape.
Q2. A square has a side of 7 cm. What is its perimeter?
Answer: B — Perimeter of square = 4 × side = 4 × 7 = 28 cm.
Q3. A rectangle has length 10 m and breadth 6 m. Its perimeter is __________ m.
Answer: B — Perimeter = 2(l + b) = 2(10 + 6) = 2 × 16 = 32 m.
Q4. A triangle has sides of length 5 cm, 6 cm, and 9 cm. What is its perimeter?
Answer: B — Perimeter of triangle = 5 + 6 + 9 = 20 cm.
Q5. A string of length 36 cm is bent to form a square. What is the side length of the square?
Answer: B — If perimeter = 36 cm, then 4 × side = 36, so side = 36 ÷ 4 = 9 cm.
Q6. Which formula gives the perimeter of a rectangle with length l and breadth b?
Answer: C — Perimeter of rectangle = 2 × (length + breadth) = 2(l + b) because opposite sides are equal.
Q7. Akshi runs around a rectangular park of length 80 m and breadth 50 m, completing 2 full rounds. What is the total distance she covers?
Answer: C — Perimeter = 2(80 + 50) = 260 m; distance in 2 rounds = 2 × 260 = 520 m.
Q8. A rectangular field has perimeter 100 m. If its length is 30 m, what is its breadth?
Answer: B — Using P = 2(l + b): 100 = 2(30 + b), so 50 = 30 + b, thus b = 20 m.
Q9. In the figure shown, the outer rectangle has length 70 m and breadth 40 m. What is the distance Akshi covers in one complete round?
Answer: B — Perimeter of rectangle = 2(70 + 40) = 2 × 110 = 220 m, which is the distance in one round.
Q10. A regular hexagon (6-sided figure) has each side of length 5 cm. What is its perimeter?
Answer: C — Perimeter of regular polygon = number of sides × length of one side = 6 × 5 = 30 cm.
What is perimeter?
Perimeter is the total distance around the outer boundary of any closed shape.
Formula for perimeter of a rectangle
Perimeter of rectangle = 2 × (length + breadth), or P = 2(l + b).
Formula for perimeter of a square
Perimeter of square = 4 × side, or P = 4s.
Formula for perimeter of a triangle
Perimeter of triangle = sum of all three sides, or P = a + b + c.
A rectangle is 8 m long and 5 m wide. What is its perimeter?
Perimeter = 2(8 + 5) = 2 × 13 = 26 metres.
A square has a side of 6 cm. What is its perimeter?
Perimeter = 4 × 6 = 24 cm.
A triangle has sides 5 cm, 7 cm, and 8 cm. What is its perimeter?
Perimeter = 5 + 7 + 8 = 20 cm.
If a wire of length 40 cm is bent into a square, what is the side length?
Side length = 40 ÷ 4 = 10 cm (because perimeter of square = 4 × side).
A rectangular park is 120 m long and 80 m wide. Usha runs around it 3 times. How far does she run?
Perimeter = 2(120 + 80) = 400 m; distance in 3 rounds = 3 × 400 = 1200 m.
Why do we use the formula 2(l + b) for rectangle instead of l + b + l + b?
Because opposite sides of a rectangle are equal in length, so we can write it as 2l + 2b = 2(l + b), which is shorter.
Define perimeter. [1 mark]
Perimeter is the total distance around the boundary of a closed shape; it is the sum of all side lengths.
A rectangular tablecloth is 4 m long and 3 m wide. Find the perimeter. Also, if lace costs ₹50 per metre, what is the cost of lacing the entire tablecloth? [2 marks]
Step 1: Calculate perimeter using P = 2(l + b) = 2(4 + 3). Step 2: Multiply perimeter by cost per metre to find total cost.
Ravi has a square garden with each side 12 m. He wants to fence it. The cost of fencing is ₹25 per metre. How much will he spend? Explain with calculation steps. [3 marks]
First find perimeter of square using P = 4 × side = 4 × 12 m. Then multiply by ₹25 per metre. Show all working steps clearly.
Two runners run on rectangular tracks. The outer track has length 70 m and breadth 40 m. The inner track has length 60 m and breadth 30 m. If the runner on the outer track completes 5 rounds and the runner on the inner track completes 8 rounds, who covers more distance and by how much? Show all your calculations. [5 marks]
Calculate perimeter of each rectangle using P = 2(l + b). Multiply each perimeter by number of rounds. Then find the difference to see who runs more.
True or False: The perimeter of a rectangle with length 8 cm and breadth 5 cm is 26 cm. Give reason for your answer. [2 marks]
Use formula P = 2(l + b) = 2(8 + 5) = 2 × 13 = 26 cm to check if statement is true or false; write clear reason.
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