Area & Perimeter
Calculate the perimeter and area of rectangles, triangles and composite shapes using the correct formulas.
Perimeter
Perimeter is the total distance around the outside of a shape. To find it, add together all the side lengths. The unit is always a length unit (cm, m, km).
Rectangle
P = 2 × (length + width)
Rectangle 8 cm × 5 cm:
P = 2 × (8 + 5) = 2 × 13 = 26 cm
Triangle
P = side1 + side2 + side3
Triangle with sides 6, 8, 10 cm:
P = 6 + 8 + 10 = 24 cm
Area Formulas
Area is the amount of space inside a shape, measured in square units (cm², m²). Each shape has its own formula.
Rectangle
A = length × width
Also: A = base × height
Triangle
A = ½ × base × height
Height must be perpendicular
Parallelogram
A = base × height
Height is perpendicular
Composite Shapes
A composite shape is made up of two or more basic shapes. To find the area, split it into simpler shapes, calculate each area separately, then add (or subtract) them.
Strategy: Split and Add
Step 1
Draw lines to divide the composite shape into rectangles and/or triangles.
Step 2
Label all measurements, including any missing lengths you can work out.
Step 3
Calculate each area separately, then add them together for the total.
Key Vocabulary
Perimeter
The total distance around the outside of a shape. Measured in length units (cm, m).
Area
The amount of space inside a shape. Measured in square units (cm², m²).
Perpendicular Height
The vertical height of a shape — measured at a right angle (90°) to the base. Used in triangle and parallelogram area formulas.
Composite Shape
A shape made by combining two or more basic shapes. Find the total area by splitting and adding the parts.
Worked Examples
Find the area and perimeter of a rectangle 9 m × 4 m.
Area: A = l × w = 9 × 4 = 36 m²
Perimeter: P = 2(9 + 4) = 2 × 13 = 26 m
Find the area of a triangle with base 10 cm and height 6 cm.
Formula: A = ½ × b × h
Substituting: A = ½ × 10 × 6 = ½ × 60 = 30 cm²
An L-shape: a 10×6 rectangle with a 4×3 rectangle removed. Find the area.
Step 1: Full rectangle area = 10 × 6 = 60 m²
Step 2: Cut-out area = 4 × 3 = 12 m²
Step 3: L-shape area = 60 − 12 = 48 m²
Knowledge Check
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Key Concepts Summary
- ●Perimeter = sum of all sides; measured in length units (cm, m).
- ●Area of a rectangle: A = l × w; measured in square units (cm², m²).
- ●Area of a triangle: A = ½ × base × perpendicular height.
- ●For composite shapes, split into simple shapes, calculate each area, then add (or subtract for cut-outs).
- ●Always include the correct units in your answer — length units for perimeter, square units for area.