Rectangle Area
A = b·hP = 2·(b+h)D = √(b²+h²)Area is base times height. Perimeter is twice the sum of the two measurements. The diagonal comes from Pythagoras: the square root of the sum of the squared sides.
The diagonal is usually the forgotten figure and it is exactly what answers the most common practical question: whether the furniture fits through the door, whether the sofa fits in the lift, whether the screen fits the recess.
Two rectangles with the same perimeter can have very different areas. One 10 by 10 and one 1 by 19 both have a perimeter of 40, but the first has an area of 100 and the second only 19.
Among all rectangles of equal perimeter, the square has the largest area. That is why rooms closer to square make better use of the wall you build.
In practice: use perimeter for skirting, framing and fencing; use area for flooring, paint and ceilings.
Area is a squared measure, so converting units means squaring the factor. One square metre is not 100 square centimetres — it is 10,000, because the factor of 100 gets squared.
This is one of the most frequent errors in construction estimates, and it is wrong by two orders of magnitude.
Keep every measurement in the same unit before calculating, and convert only the result.
Frequently asked questions
Calculate the area and add a margin for cuts and breakage, usually 10%. Large tiles or diagonal laying need a bigger margin.
Because area conversion squares the factor. A metre is 100 centimetres, so a square metre is 100 times 100, that is 10,000 square centimetres.
To know whether something fits through an opening. It is the greatest distance between two points of the rectangle, and what determines whether a rigid object fits when tilted.
Work out the total wall area and subtract the window and door areas. For painting, that is what determines the real amount of paint.