Area and Perimeter of a Rectangle

Calculates the area of a rectangle as height × width.

Explanation

A rectangle is a quadrilateral with four right angles. Its two side lengths give you both the area and the perimeter.

S = a b \qquad L = 2(a + b)

$S$ — the area
$L$ — the perimeter
$a$ — the height, the vertical side
$b$ — the width, the horizontal side

Example

With the defaults, a height of $a = 4$ and a width of $b = 6$ :

S = 4 \times 6 = 24

The perimeter adds one height and one width, then doubles the result:

L = 2 \times (4 + 6) = 20

So the area is 24 and the perimeter is 20.

Why multiplying the sides works

Picture the rectangle as a grid of unit squares: 4 rows of 6 squares each. Counting them gives $4 \times 6 = 24$ squares, and that count is the area.

Watch out

The perimeter does not determine the area. Among rectangles of perimeter 20 you can find 4 by 6 (area 24), 1 by 9 (area 9) and 5 by 5 (area 25). For a fixed perimeter, the closer the rectangle is to a square, the larger its area. Make sure both sides are given in the same unit.