Key Points

The area of a rectangle is the product of its length and width. The formula is $A = l \times w$, where $l$ is the length and $w$ is the width. Area is measured in square units, such as $\text{cm}^2$ or $\text{m}^2$.

A square is a special rectangle where all sides are equal. Its area is calculated as $A = s^2$, where $s$ is the length of one side.

The area of any triangle is half the product of its base and corresponding height. The formula is $A = \frac{1}{2} \times b \times h$, where $b$ is the base and $h$ is the perpendicular height from the base to the opposite vertex.

The area of a parallelogram is the product of its base and the corresponding perpendicular height. The formula is $A = b \times h$, where $b$ is the length of the base and $h$ is the height.

The area of a rhombus can be found using its diagonals. The formula is $A = \frac{1}{2} \times d_1 \times d_2$, where $d_1$ and $d_2$ are the lengths of the two diagonals.

The area of a trapezium (or trapezoid) is half the product of its height and the sum of its parallel sides. The formula is $A = \frac{1}{2} \times h \times (a+b)$, where $a$ and $b$ are the lengths of the parallel sides and $h$ is the perpendicular height between them.

To find the area of any irregular polygon, you can divide it into smaller, non-overlapping shapes like triangles and rectangles. The total area is the sum of the areas of these individual shapes.

Do not confuse perimeter with area. Two shapes can have the same perimeter but different areas, or the same area but different perimeters. A larger perimeter does not necessarily mean a larger area.

A median of a triangle, which is a line segment from a vertex to the midpoint of the opposite side, divides the triangle into two smaller triangles of equal area.

Triangles that share the same base and have their third vertices on a line parallel to the base have equal areas. This is because they have the same base and the same height.

To find the area of a path or border around a shape, calculate the area of the outer shape and subtract the area of the inner shape. The formula is Area of Path = Area(Outer) - Area(Inner).

If the area of a shape and some of its dimensions are known, the area formula can be rearranged to find a missing dimension. For example, for a triangle, if Area $A$ and base $b$ are known, the height is $h = \frac{2A}{b}$.