Solved Practical Perimeter Problems with Step-by-Step Explanations

📚 What is Perimeter?

Perimeter is the total distance around the outside of a two-dimensional shape. Think of it like building a fence around a yard – you need to know the perimeter to know how much fencing you need. To find the perimeter, you simply add up the lengths of all the sides.

• 📏 Basic Formula: For a shape with sides $a$, $b$, $c$, and so on, the perimeter ($P$) is: $P = a + b + c + ...$
• 📐 Rectangle: A rectangle has two pairs of equal sides (length $l$ and width $w$). The perimeter is: $P = 2l + 2w$
• 🔶 Square: A square has four equal sides ($s$). The perimeter is: $P = 4s$

➕ Example 1: The Rectangular Garden

A rectangular garden is 10 meters long and 5 meters wide. What is the perimeter of the garden?

1. Identify:
   • Length ($l$) = 10 meters
   • Width ($w$) = 5 meters
2. Apply the formula:
   • $P = 2l + 2w$
   • $P = 2(10) + 2(5)$
   • $P = 20 + 10$
   • $P = 30$ meters
3. Answer: The perimeter of the garden is 30 meters.

🌳 Example 2: The Square Park

A square park has sides that are each 25 meters long. What is the perimeter of the park?

1. Identify:
   • Side ($s$) = 25 meters
2. Apply the formula:
   • $P = 4s$
   • $P = 4(25)$
   • $P = 100$ meters
3. Answer: The perimeter of the park is 100 meters.

🏡 Example 3: A Complex Shape

Imagine a shape with sides measuring 3cm, 4cm, 5cm, 6cm and 7cm. What is the perimeter?

1. Identify:
   • Sides: 3cm, 4cm, 5cm, 6cm, 7cm
2. Apply the formula:
   • $P = 3 + 4 + 5 + 6 + 7$
   • $P = 25$ cm
3. Answer: The perimeter is 25 cm.

✍️ Practice Quiz

Solve these perimeter problems. Answers are provided below!

1. Question 1: A rectangle has a length of 12 cm and a width of 8 cm. What is its perimeter?
2. Question 2: A square has a side length of 7 meters. What is its perimeter?
3. Question 3: A triangle has sides of 5 inches, 12 inches, and 13 inches. What is its perimeter?
4. Question 4: A room is 15 feet long and 10 feet wide. You want to put baseboard around the room. How much baseboard do you need?
5. Question 5: A farmer wants to fence a rectangular field that is 40 meters long and 25 meters wide. How much fencing is required?
6. Question 6: The perimeter of a square is 36 inches. How long is each side?
7. Question 7: An irregular shape has sides of 2cm, 3cm, 4cm, 5cm, and 6cm. What is the perimeter?

✅ Answers to the Practice Quiz

1. Answer 1: $P = 2(12) + 2(8) = 24 + 16 = 40$ cm
2. Answer 2: $P = 4(7) = 28$ meters
3. Answer 3: $P = 5 + 12 + 13 = 30$ inches
4. Answer 4: $P = 2(15) + 2(10) = 30 + 20 = 50$ feet
5. Answer 5: $P = 2(40) + 2(25) = 80 + 50 = 130$ meters
6. Answer 6: $s = 36 / 4 = 9$ inches
7. Answer 7: $P = 2 + 3 + 4 + 5 + 6 = 20$ cm