Area and Perimeter of Shapes
Area is the space inside a shape (measured in cm², m²). Perimeter is the total distance around the outside. Think of area as how much carpet you need and perimeter as how much fencing.
Key Formulas
- Rectangle: Area = length × width | Perimeter = 2(length + width)
- Triangle: Area = ½ × base × height
- Circle: Area = πr² | Circumference = 2πr
Rectangles (and Squares)
A rectangle is the easiest shape. Multiply the two different sides for area. Add all four sides for perimeter (or use the shortcut: double the length, double the width, add them together).
Worked Example
A room is 5 m long and 3 m wide.
- Area = 5 × 3 = 15 m²
- Perimeter = 2(5 + 3) = 2 × 8 = 16 m
Triangles
A triangle is exactly half of a rectangle. That’s why we use ½ × base × height. The heightmust be the perpendicular height (straight up from the base), not the slanted side.
Worked Example
A triangle has a base of 8 cm and a height of 6 cm.
Area = ½ × 8 × 6 = 24 cm²
Circles
The radius (r) is the distance from the centre to the edge. The diameter is all the way across (twice the radius). Use π ≈ 3.14 unless the question says otherwise.
Worked Example
A circular pond has radius 4 m.
- Area = π × 4² = 3.14 × 16 = 50.24 m²
- Circumference = 2 × π × 4 = 25.12 m
Compound Shapes
A compound (or composite) shape is made of simpler shapes stuck together. The trick is to split it into rectangles(or triangles), find each area separately, then add them up.
Worked Example
An L-shaped room: the top part is 6 m × 2 m; the bottom part is 4 m × 3 m.
- Top rectangle: 6 × 2 = 12 m²
- Bottom rectangle: 4 × 3 = 12 m²
- Total area = 12 + 12 = 24 m²
Real-World Examples
- Carpet for a room: You need the area. A room 4 m × 3.5 m needs 14 m² of carpet.
- Fence around a garden: You need the perimeter. A garden 10 m × 8 m needs 2(10 + 8) = 36 m of fencing.
Common Mistakes
- Mixing up area and perimeter (area is space inside, perimeter is distance around).
- Using the slanted side instead of the perpendicular height for triangles.
- Forgetting to halve the diameter to get the radius for circles.
- Missing a section when splitting compound shapes.
Practice Questions
- Find the area and perimeter of a rectangle 12 cm by 5 cm.
- A triangle has base 10 cm and height 7 cm. What is its area?
- A circle has diameter 14 cm. Find its area. (Use π = 3.14)
- An L-shape: bottom rectangle 8 m × 3 m, top rectangle 4 m × 2 m. Total area?
- A garden is 15 m long and 9 m wide. How much fencing is needed to go all the way around?
Answers: 1) 60 cm², 34 cm 2) 35 cm² 3) 153.86 cm² 4) 32 m² 5) 48 m