🔵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.
👀 See a worked example
🤖 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.
👀 See a worked example
🤖 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.
👀 See a worked example
🤖 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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