Area – How Much Space a Shape Covers
Area measures how much flat space a shape covers. It is one of the most practical measurements in everyday life — from tiling a floor and painting a wall to calculating the size of a solar panel or a sports pitch.
What Is Area?
Area is measured in square units: cm², m², km². It tells you how many unit squares fit inside a shape. Area is always a positive number.
Area Formulas for Common Shapes
| Shape | Formula | Variables |
|---|---|---|
| Square | A = s² | s = side length |
| Rectangle | A = l × w | l = length, w = width |
| Triangle | A = ½ × b × h | b = base, h = perpendicular height |
| Parallelogram | A = b × h | b = base, h = perpendicular height |
| Trapezium | A = ½(a + b) × h | a, b = parallel sides, h = height |
| Circle | A = πr² | r = radius |
| Sector | A = (θ/360) × πr² | θ = angle in degrees |
| Kite or Rhombus | A = ½ × d₁ × d₂ | d₁, d₂ = diagonals |
Worked Examples
Find the area of a triangle with base 12 cm and height 7 cm.
A = ½ × 12 × 7 = 42 cm².
Find the area of a trapezium with parallel sides 5 cm and 9 cm, height 4 cm.
A = ½(5 + 9) × 4 = ½ × 14 × 4 = 28 cm².
Find the area of a circle with diameter 14 cm.
r = 7 cm. A = π × 49 = 49π ≈ 153.94 cm².
Area of Compound Shapes
Split the shape into simpler known shapes, calculate each area, then add (or subtract) them.
A shape is a rectangle 10 × 6 with a semicircle of diameter 6 on top. Find the total area.
Rectangle: 10 × 6 = 60. Semicircle: ½π(3)² = 4.5π ≈ 14.14. Total: ≈ 74.14 cm².
Key Takeaways
- Area is always in square units (cm², m², etc.).
- Triangle: ½bh. Rectangle: lw. Circle: πr². Trapezium: ½(a+b)h.
- For compound shapes: split, calculate each part, add or subtract.
- Always use the perpendicular height, not the slant side.
Practice Questions
- Find the area of a parallelogram with base 15 cm and perpendicular height 8 cm.
- A triangle has base 20 cm and area 90 cm². Find its height.
- Find the area of a sector with radius 6 cm and angle 120°. Leave answer in terms of π.
- A room is 5 m by 4 m with a rectangular alcove 1 m by 2 m cut out of one corner. Find the floor area.
- A rhombus has diagonals 10 cm and 14 cm. Find its area.