A rectangle’s area measures the flat surface inside its four sides. Multiply two adjacent side lengths to find it. Its perimeter measures the boundary instead, while its diagonal joins opposite vertices. These three quantities answer different questions and use different calculations.
Which measurements belong in the area formula?
A rectangle has four right angles and equal opposite sides. Choose any side as the base b; the adjacent perpendicular side is the height h. The base does not have to be the longer side. Rotating the rectangle changes its position, not its area.
The first formula gives area, the second perimeter and the third diagonal length. Use the same length unit for b and h before substituting. Multiplying centimetres by centimetres gives square centimetres, whereas adding side lengths still gives centimetres.
Worked example: a rectangle measuring 20 cm by 8 cm
First multiply the base, 20 cm, by the height, 8 cm. The result is the area. Next add the two different side lengths and double that sum, because each appears twice on the boundary. Finally apply the Pythagorean theorem to either triangle formed by the diagonal.
The surface covers 160 square centimetres and the boundary measures 56 cm. The diagonal is approximately 21.54 cm; its exact form is shown before the rounded value. Keeping the square root until the last step avoids accumulating rounding errors.
How do you recover a missing side?
If you know the area and one side, divide the area by that side. This reverses multiplication. For example, dividing an area of 160 square centimetres by a base of 20 cm gives a height of 8 cm.
This calculation assumes a genuine rectangle. For a slanted parallelogram, the height is the perpendicular distance between its parallel bases, not the sloping side. For the relationship between covering a surface and measuring its edge, see area and perimeter.
