Why Area and Perimeter Matter
Imagine you're painting a wall, laying tiles on a floor, or fencing a garden. You need to know two things:
- How much surface you need to cover → this is the area
- How much edging or border you need → this is the perimeter
The total distance around the outside of a 2D shape, measured in units of length (cm, m, km, etc.).
The amount of surface enclosed by a 2D shape, measured in square units (cm², m², km², etc.).
Think of perimeter as the length of fence you'd need to go around a field, and area as the amount of grass seed you'd need to cover the field.
Throughout this topic, we'll build up from triangles to parallelograms, trapeziums, and then combine shapes into compound figures and paths.
Area and Perimeter of a Triangle
Every triangle — whether it's right-angled, isosceles, equilateral, or scalene — uses the same area formula.
Any one side of the triangle that you choose to measure from.
The perpendicular (right-angle) distance from the base to the opposite vertex. This is NOT a slanted side — it must form a 90° angle with the base.
Area of a triangle:
where = base and = perpendicular height.
Perimeter of a triangle:
where , , and are the three side lengths.
The formula works because every triangle is exactly half of a rectangle (or parallelogram) with the same base and height.
A very common mistake is using a slant height instead of the perpendicular height. Always check that the height line meets the base at 90°. Look for the small square symbol that marks a right angle.
11 more sections in this topic
Pick this up in your Library: it holds the whole topic, notes, cheatsheet and questions.