Rectangle Area

Length times width is the most fundamental area formula there is: a rectangle 4 units long and 3 units wide tiles perfectly into 4 × 3 = 12 unit squares, and counting those squares is the area. A painter uses it constantly — a wall 4 m long and 2.5 m high presents 10 m² of surface, and at a typical coverage of 10 m² per litre, that wall costs exactly one litre of paint per coat.

Every other area formula is built on this one. A parallelogram is a sheared rectangle, a triangle is half of one, and even the areas of curved shapes are found by slicing them into ever-thinner rectangular strips — the idea at the heart of integral calculus. Watch the units: multiplying two lengths gives a squared unit, so metres in means square metres out, and mixing feet with metres without converting first is the classic mistake.