Area Formulas
Every straight-sided area formula is a variation on base times height. A rectangle uses it directly, a triangle is half of one, and a trapezoid averages its two parallel sides to get an effective base.
Formulas
Triangle: A = ½ × b × h
Circle: A = πr²
Trapezoid: A = ½ × (a + b) × h
Parallelogram: A = b × h
Ellipse: A = π × a × b
The height in the triangle, trapezoid, and parallelogram formulas is always the perpendicular distance between the base and the opposite vertex or side — never the length of a sloping edge. Using a slanted side instead of the true height is the most common source of a wrong answer, and it always overestimates the area.
Converting Area Units
Area conversion factors are the square of the length factors, which trips people up regularly. A yard is 3 feet, but a square yard is 9 square feet, not 3.
1 square metre = 10.7639 square feet
Because one metre is 3.28084 feet, and 3.28084 squared is 10.7639. To go from square feet to square metres, divide by the same number.
1 square yard = 9 square feet
Carpet and turf are commonly priced per square yard in the US and per square metre elsewhere. Convert before comparing quotes or the cheaper-looking option may not be.
1 acre = 43,560 square feet = 4,046.86 square metres
A hectare is 10,000 square metres, roughly 2.471 acres. Both are area units defined without reference to any particular shape.
Measuring Irregular Spaces
Real rooms, gardens, and plots rarely match a textbook shape. The standard approach is decomposition: split the space into rectangles and triangles, calculate each separately, and add the results. Subtract rather than add for cut-outs such as a chimney breast or a pond.
For flooring, paint, and turf, add a waste allowance on top of the calculated area — typically 5% for a simple rectangular room and 10-15% where there are diagonal cuts, patterned material that needs matching, or many obstacles. The area calculation gives you the true surface; the allowance covers what gets trimmed off and thrown away.