Perimeter

Standard Formulas

• Rectangles: The perimeter is the sum of two lengths and two widths, expressed as $P = 2l + 2w$ or $P = 2(l + w)$.
• Squares: Since all four sides are equal, the formula is $P = 4s$, where $s$ is the side length.
• Circles: The circumference is calculated using $C = 2\pi r$ (where $r$ is radius) or $C = \pi d$ (where $d$ is diameter).

Compound Shapes

• To find the perimeter of a compound (composite) shape, you must identify all external side lengths. Often, some lengths are 'missing' and must be deduced from the properties of the shape (e.g., opposite sides of a rectangle being equal).
• Internal lines must be ignored. Only the segments that form the outer boundary contribute to the perimeter calculation.

• It is vital to distinguish between Perimeter and Area, as they measure different physical properties and use different units.

• Check for Missing Sides: In compound shapes, examiners often omit one or two side lengths. Use horizontal and vertical logic (the sum of smaller segments must equal the total length of the parallel opposite side) to find these before adding.

• Unit Consistency: Always verify that all side lengths are in the same units before calculating. If one side is in cm and another in mm, convert them to a single unit first to avoid calculation errors.

• Identify Equal Sides: Look for 'dashes' on diagrams which indicate sides of equal length. This is a common way to provide information about isosceles triangles or regular polygons without explicitly stating every number.

• Sanity Check: For a rectangle, the perimeter should always be more than twice the longest side. If your calculated perimeter is smaller than the longest side, a calculation error has occurred.