Area and Perimeter

What is Perimeter?

Perimeter is the distance AROUND the outside of a shape.

Think of it like a fence around your yard - you're measuring the total length of the fence!

How to find perimeter: Add up ALL the side lengths

Perimeter of Common Shapes

Rectangle:

• Perimeter = Length + Length + Width + Width
• Or: P = 2 × Length + 2 × Width
• Or: P = 2(L + W)

Example: Rectangle with L = 8 cm, W = 5 cm

• P = 8 + 8 + 5 + 5 = 26 cm
• OR P = 2(8) + 2(5) = 16 + 10 = 26 cm ✓

Square:

• All four sides are equal!
• Perimeter = Side + Side + Side + Side
• Or: P = 4 × Side

Example: Square with side = 6 inches

• P = 6 + 6 + 6 + 6 = 24 inches
• OR P = 4 × 6 = 24 inches ✓

Triangle:

• Perimeter = Side 1 + Side 2 + Side 3
• Add all three sides

Example: Triangle with sides 5 cm, 7 cm, 9 cm

• P = 5 + 7 + 9 = 21 cm ✓

Any polygon:

• Just add up ALL the sides!

What is Area?

Area is the amount of space INSIDE a shape.

Think of it like covering your floor with tiles - how many tiles do you need?

Units for area: Always SQUARE units

• Square inches (in²)
• Square feet (ft²)
• Square centimeters (cm²)
• Square meters (m²)

Area of Common Shapes

Rectangle:

• Area = Length × Width
• A = L × W

Example: Rectangle 8 cm by 5 cm

• A = 8 × 5 = 40 cm² ✓

Square:

• Area = Side × Side
• A = s × s = s²

Example: Square with side 6 inches

• A = 6 × 6 = 36 in² ✓

Triangle:

• Area = ½ × Base × Height
• A = ½ × b × h

Important: Height must be perpendicular (straight up) from the base!

Example: Triangle with base 10 ft, height 6 ft

• A = ½ × 10 × 6 = ½ × 60 = 30 ft² ✓

Perimeter vs Area - What's the Difference?

Perimeter:

• Measures the OUTSIDE (distance around)
• Uses regular units (cm, in, ft)
• Like putting a ribbon around a present

Area:

• Measures the INSIDE (space covered)
• Uses SQUARE units (cm², in², ft²)
• Like putting wrapping paper ON a present

Real-World Examples

Perimeter:

• Fence around a garden
• Border around a picture frame
• Track around a playground
• Trim around a room

Area:

• Carpet needed for a floor
• Paint needed for a wall
• Grass seed for a lawn
• Fabric for a blanket

Problem-Solving Strategy

For perimeter problems:

1. Find all the side lengths
2. Add them all up
3. Use the correct unit (no squared!)

For area problems:

1. Identify the shape
2. Find the measurements you need
3. Use the correct formula
4. Don't forget square units!

Composite Shapes

What if the shape isn't simple?

For perimeter:

• Add up ALL the outside edges
• Don't count inside edges!

For area:

• Break the shape into rectangles
• Find the area of each piece
• Add the areas together

Example: L-shaped figure

• Break into two rectangles
• Rectangle 1: 4 × 3 = 12 cm²
• Rectangle 2: 6 × 2 = 12 cm²
• Total area: 12 + 12 = 24 cm² ✓

Estimating Area

You can count squares!

• Draw a grid over the shape
• Count full squares
• Estimate partial squares (two halves = one whole)
• Add them up

Practice Tips

Remember:

• Perimeter = ADD all sides (around the outside)
• Area = MULTIPLY length × width (inside space)
• Always use the right units!
• Draw a picture to help visualize

Check your work:

• Does your answer make sense?
• Did you use square units for area?
• Did you add all the sides for perimeter?

Common Mistakes

❌ Using square units for perimeter ❌ Adding sides for area ❌ Forgetting to multiply by ½ for triangle area ❌ Using the slant height instead of perpendicular height for triangles

✅ Perimeter = add (regular units) ✅ Area = multiply (square units) ✅ Triangle area needs perpendicular height ✅ Double-check your formula!