Area of a Polygon (Grade 11 NSC Matric Mathematics): Revision Notes

Area of a Polygon

A polygon is a closed shape made up of straight lines. Understanding how to calculate the area of different polygons is essential for solving many geometry problems. The area represents the amount of space inside a shape, usually measured in square units.

Basic polygon area formulas

Square

A square has four equal sides. When you know the length of one side, you can find the area easily.

Formula: Area = $s^2$

Where $s$ is the length of any side.

Rectangle

A rectangle has opposite sides that are equal in length. You need to know both the length and width to calculate the area.

Formula: Area = $b \times h$

Where $b$ is the base (length) and $h$ is the height (width).

Triangle

The area of any triangle depends on its base and the perpendicular height from that base to the opposite vertex.

Formula: Area = $\frac{1}{2}b \times h$

Where $b$ is the base and $h$ is the perpendicular height.

Trapezium

A trapezium has one pair of parallel sides. The area formula uses both parallel sides and the perpendicular distance between them.

Formula: Area = $\frac{1}{2}(a + b) \times h$

Where $a$ and $b$ are the lengths of the parallel sides, and $h$ is the perpendicular height between them.

Parallelogram

A parallelogram has two pairs of parallel sides. Like a rectangle, but the angles don't have to be 90 degrees.

Formula: Area = $b \times h$

Where $b$ is the base and $h$ is the perpendicular height (not the slanted side length).

Circle

A circle's area depends on its radius - the distance from the centre to any point on the circle.

Formula: Area = $\pi r^2$

Circumference: $2\pi r$

Where $r$ is the radius.

Worked example: Finding the area and perimeter of a parallelogram

Let's work through a complete problem that shows how to find both area and perimeter of a parallelogram.