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Class 4 Maths Adventure

Area and Perimeter Formulas

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Hi! I'm Vidi. Let's learn Area and Perimeter Formulas together — read with me, then play the games to win a ⭐!

🔵Perimeter of Rectangle and Square

Perimeter is the total distance around the outside of a shape — like walking around the boundary of a park.

Rectangle:
Perimeter = 2 x (Length + Width)
P = 2 x (l + w)

Why? A rectangle has 2 equal lengths and 2 equal widths.

Square:
All four sides are equal.
Perimeter = 4 x side (P = 4s)

To find a missing side: rearrange the formula. E.g. if P = 36 and l = 10, then 36 = 2(10+w), so w = 8.

Perimeter FormulasRectangleLength = 8 cmW=5P = 2(8+5) = 26 cmSquare6 cmP = 4 x 6 = 24 cm6 cm
👀 See a worked example
A rectangular garden is 12 m long and 8 m wide. Find its perimeter. P = 2 x (l + w) = 2 x (12 + 8) = 2 x 20 = 40 m. Answer: 40 m.
A square playground has a side of 25 m. What is its perimeter? P = 4 x s = 4 x 25 = 100 m. Answer: 100 m.
A rectangle has a perimeter of 36 cm. Its length is 10 cm. Find the width. P = 2(l + w). 36 = 2(10 + w). 18 = 10 + w. w = 18 - 10 = 8 cm. Answer: 8 cm.

🤖 Vidi's Key Points

  • Perimeter measures the distance AROUND the boundary of a shape
  • Rectangle: P = 2 x (l + w) because it has 2 lengths and 2 widths
  • Square: P = 4 x s because all four sides are equal
  • To find missing side: rearrange the perimeter formula

🟢Area of Rectangle and Square

Area is the amount of space INSIDE a shape. Think of it as the number of 1x1 squares that can fit inside.

Rectangle:
Area = Length x Width (A = l x w)

Square:
Area = side x side (A = s x s = s²)

Units: perimeter uses cm/m, but area uses square units — cm² or m².

To find a missing side when area is given: divide. E.g. if A = 54, l = 9, then w = 54 / 9 = 6.

Area = Count the squares inside!3 x 2 = 6 squaresArea = 6 sq unitsArea FormulasRectangle: A = l x wSquare: A = s x s = s
👀 See a worked example
A rectangular hall is 15 m long and 10 m wide. Find its area. A = l x w = 15 x 10 = 150 m². Answer: 150 square metres.
A square tile has a side of 30 cm. What is its area? A = s x s = 30 x 30 = 900 cm². Answer: 900 square centimetres.
A rectangle has an area of 54 cm². Its length is 9 cm. Find its width. A = l x w. 54 = 9 x w. w = 54 / 9 = 6 cm. Answer: width = 6 cm.

🤖 Vidi's Key Points

  • Area measures the space INSIDE a shape
  • Rectangle: A = l x w (length times width)
  • Square: A = s x s (side squared)
  • Area is always measured in square units: cm² or m²

🟣Relationship Between Area and Perimeter

Area and perimeter are related but measure different things:

  • Perimeter = distance around (units: cm, m)
  • Area = space inside (square units: cm², m²)

Two shapes can have the same perimeter but different areas, or the same area but different perimeters!

This is an important insight: a square always has the largest area for a given perimeter compared to other rectangles.

Same Perimeter = 24 m, Different Areas!10m x 2mArea = 20 m2P = 24 m8m x 4mArea = 32 m2P = 24 m6m x 6mArea = 36 m2P = 24 mSquare has the LARGEST area for the same perimeter!
👀 See a worked example
A square has a perimeter of 48 cm. Find its area. Step 1: Find side from perimeter. P = 4s. 48 = 4s. s = 12 cm. Step 2: Find area. A = s x s = 12 x 12 = 144 cm².
A square has an area of 64 m². Find its perimeter. Step 1: Find side from area. A = s x s. 64 = s x s. s = 8 m (since 8 x 8 = 64). Step 2: Find perimeter. P = 4 x 8 = 32 m.
A farmer has a rectangular field 10 m x 25 m. Fencing costs Rs.15 per metre. Find the fencing cost and area of the field. Perimeter = 2(10+25) = 2 x 35 = 70 m. Fencing cost = 70 x 15 = Rs.1,050. Area = 10 x 25 = 250 m².

🤖 Vidi's Key Points

  • Same perimeter does NOT mean same area!
  • Square gives the largest area for a given perimeter
  • Perimeter units: cm, m (linear); Area units: cm2, m2 (square)
  • To find perimeter from area: first find the side, then use the formula

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