Knowledge Organiser: Area of Rectangles & Triangles
Key Terms
- Area: The amount of space a shape covers, measured in square units
- Perpendicular height: The height at 90° to the base: NOT the slant side
- Base: The bottom side of a shape used in area calculations
- Composite shape: A shape made from two or more simpler shapes
Must-Know Facts
- Area is always in square units: cm², m², mm²
- Triangle area = ½ × rectangle area with same base and height
- Height MUST be perpendicular (90°) to the base
- For composite shapes: split into simpler parts, find each area, then add or subtract
- To find a missing side: rearrange the formula (e.g. l = Area ÷ w)
Key Formulas
- Rectangle: A = l × w
- Square: A = s²
- Triangle: A = ½ × b × h
- Missing side: side = Area ÷ other side
Common Mistakes
- Forgetting the ½ in triangle area: A = ½ × base × height: the ½ is always required
- Height must be perpendicular: The height is the perpendicular distance to the base, not the slant side
- Units: Area is always cm², m², etc.: never just cm or m
- Composite shapes: Split into rectangles and triangles, calculate each area separately, then add or subtract
Worked Examples
Find the area of a rectangle with length 8 cm and width 5 cm. Step 1 Write the formula Area = length × width Step 2 Substitute and calculate Area = 8 × 5 = 40 cm²
Worked Examples
Find the area of a triangle with base 12 cm and perpendicular height 7 cm. Step 1 Write the formula Area = ½ × base × height Step 2 Substitute values Area = ½ × 12 × 7 Step 3 Calculate Area = ½ × 84 = 42 cm² Or: 12 × 7 = 84, then 84 ÷ 2 = 42
Worked Examples
A rectangle has area 48 cm² and width 6 cm. Find the length. Step 1 Write what we know Area = length × width 48 = length × 6 Step 2 Rearrange to find length length = 48 ÷ 6 = 8 cm