Area explained

Area is measured in square metres (m²).

It is important to realise that m are not the same as m².

The area of a triangle is half the area of the smallest rectangle that will enclose it, and so the area of the triangle is half the area of that rectangle.

A parallelogram has two pairs of parallel sides. Imagine chopping a right angle triangle off one end of the parallelogram and putting it on the other end to make a rectangle. It's particlarly important to remember to use the perpendicular height for this calculation because parallelograms look similar to rectangles.

A trapezium has one pair of parallel sides. By taking the average length of the parallel sides we are effectively turning the calculation into the area of a rectangle with the same area.

To find the area of a circle we need to use pi. The area of a square with each side of length r will have area r². The proportion of that square covered by a quarter of a circle happens to work out to ^π/₄, so the area of the quarter circle is ^π/₄ times r². This means a whole circle's area is πr².

Calculating area of rectangular-ish stuff

All the base and height dimensions being multiplied by each other below are at right angles to each other – sometimes called the perpendicular height.

Area of a rectangle:

base x height
[or] length x width

Area of a triangle:

¹/₂ base x height

Area of a parallelogram:

base x perpendicular height

Area of a trapezium:

¹/₂ (a + b) x height

Calculating area of circles and spheres

Area of a circle:

pi x radius²
π·r²

Surface area of a sphere:

4·π·r²