🔢 MathGrade 4Lesson 27
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Measure Area and Perimeter

Lesson preview: the Mini Lesson and Vocabulary are open to everyone. Guided practice, exercises, the parent checklist and the printable PDF worksheet come with full access (free 7-day trial or membership).

Learning Objectives

  • 1Calculate the perimeter of rectangles and polygons in both customary (in, ft) and metric (cm, m) units
  • 2Calculate the area of rectangles using length × width and report it in square inches, square feet, square centimeters, or square meters
  • 3Apply area and perimeter formulas to real-life problems in both US customary and metric units
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Mini Lesson

Perimeter and area are two ways to measure a shape. Perimeter tells us the total distance around the outside of a shape. Area tells us how much space is inside a shape. Both measurements are used every day — when fencing a garden, tiling a floor, or planning a room layout. In the US we measure small things in inches and large things in feet; the rest of the world (and science) uses centimeters and meters. Both systems work the same way — only the unit label changes.

Perimeter (Distance Around)

  • Perimeter = the distance around a shape; add all the side lengths together.
  • Rectangle perimeter: P = 2 × (length + width), or P = 2l + 2w.
  • Square perimeter: P = 4 × side (since all four sides are equal).
  • For any polygon: add all side lengths — P = a + b + c + ...
  • Customary example: a desk top 24 in by 18 in has P = 2 × (24 + 18) = 84 in.
  • Metric example: a desk top 60 cm by 45 cm has P = 2 × (60 + 45) = 210 cm.
  • Use feet for room-sized perimeters and meters for large outdoor areas; perimeter keeps the same units as the sides (in, ft, cm, or m).

Area (Space Inside)

  • Area = the amount of space inside a shape; measured in SQUARE units.
  • Customary area units: square inches (sq in), square feet (sq ft), square yards (sq yd).
  • Metric area units: square centimeters (cm²), square meters (m²).
  • Rectangle area: A = length × width.
  • Square area: A = side × side = s².
  • Imagine filling the shape with unit squares — the total count is the area.
  • Customary example: a carpet 12 ft × 9 ft has A = 12 × 9 = 108 sq ft.
  • Metric example: a carpet 3.7 m × 2.7 m has A ≈ 10 m².

Choosing the Right Unit

  • Desk- or book-sized: inches or centimeters.
  • Room- or floor-sized: feet or meters.
  • Yard- or field-sized: yards (or feet) and meters.
  • Never mix systems in one calculation — keep the entire problem in inches OR cm, in feet OR m.
Perimeter in feet and metersCarpet Perimeter: P = 2(l + w)l = 12 ft (US)l = 3.7 m (SI)w=9 ftw=2.7m9 ft2.7 mUS: P = 2 x (12 + 9) = 42 ftSI: P = 2 x (3.7 + 2.7) = 12.8 m
Area in US customary and metric unitsArea: A = l x w (square units)SystemSmall AreaLarge AreaUS Customarysq in (book)sq ft (room)Metric (SI)cm² (book)m² (room)l = 8w=324 squares8 x 3 = 24 sq in8 x 3 = 24 cm²Same math — different scale.
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Tip: remember the difference — perimeter is the path around the outside (like a fence), while area is the space inside (like a floor). Perimeter uses plain units (in, ft, cm, m); area always uses SQUARE units (sq in, sq ft, cm², m²).

Vocabulary
Perimeter
The total distance around the outside of a flat shapee.g. The perimeter of a 3 ft x 4 ft rectangle is 14 ft.
Area
The amount of flat space inside a shape, in square unitse.g. The area of a 3 ft x 4 ft rectangle is 12 sq ft.
Length
How long a side or distance ise.g. The length of my pencil case is 20 cm (about 8 in).
Width
How wide a shape is, measured at right angles to the lengthe.g. The width of the rectangle is 3 ft.
Square inch (sq in)
A US customary unit of area — a 1 inch by 1 inch squaree.g. A postage stamp has an area of about 1 sq in.
Square foot (sq ft)
A US customary unit of area — a 1 ft by 1 ft square; used for roomse.g. A 10 ft by 12 ft bedroom has 120 sq ft.
Square centimeter (cm²)
A metric unit of area — a 1 cm by 1 cm squaree.g. A button covers about 1 cm².
Square meter (m²)
A metric unit of area — a 1 m by 1 m square; used for rooms and gardense.g. A small kitchen has about 8 m².
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