Area and perimeter.

Imagine fencing a garden and then covering its soil with turf. The fence follows the boundary, so it measures perimeter. The turf covers the inside, so it measures area. These are different quantities even for the same shape.

Perimeter adds boundary lengths and uses length units. Area counts square units and uses products of lengths. Start with a rectangle tiled by rows and columns of unit squares, then see how cutting or rearranging it leads to the other area formulas.

Area formulas require particular dimensions, not just any two visible lengths. In a triangle or parallelogram, the height measures the perpendicular separation from the chosen base to the opposite point or side.

A sloping side is not automatically the height. Draw the perpendicular if it is missing. For a trapezium, identify the parallel sides before averaging their lengths. Naming the correct base and height is often more important than the final arithmetic.

A result should communicate what was measured. A perimeter of 20 means little without a unit; an area written as 20 cm confuses a two-dimensional measure with a length.

Check units before and after applying a formula. A product of two lengths should produce square units, while a sum of boundary lengths stays in ordinary length units. Also make a rough size estimate from a surrounding rectangle or familiar shape to detect an impossible answer.

Mark all boundary segments for perimeter, including any sides that must first be deduced. For area, identify a valid shape formula and its perpendicular dimensions.

Keep the two calculations separate and label their units. If the question gives mixed units, convert before substituting rather than attaching a desired unit to an inconsistent product.