Perimeter and Area - Perimeter and Area of Squares and Rectangles

Perimeter is the total length of the boundary of a closed figure. For a square or rectangle, you can visualize this as the length of a wire needed to form the shape's outline.

Area measures the surface region enclosed by the boundaries of a closed figure. If you were to tile a floor, the number of unit squares required to cover the entire floor represents its area.

A Square is a quadrilateral where all four sides are equal and every interior angle is $90^\circ$. Visually, it is perfectly symmetrical, and its perimeter is simply four times the length of one side.

A Rectangle is a quadrilateral where opposite sides are equal and every interior angle is $90^\circ$. It has a longer dimension called length ($l$) and a shorter dimension called breadth ($b$).

Units of Measurement: Perimeter is measured in linear units like $cm$ or $m$. Area is measured in square units like $cm^{2}$ or $m^{2}$. Note that $1 m^{2} = 10,000 cm^{2}$ because area involves two dimensions ($100 cm \times 100 cm$).

To find a missing dimension of a rectangle when the area and one side are given, use the inverse operation: $length = \frac{Area}{breadth}$ or $breadth = \frac{Area}{length}$.

The perimeter and area change differently when side lengths are adjusted. For example, doubling the side of a square doubles its perimeter but quadruples its area ($2s \times 2s = 4s^{2}$).