Mathematical Concepts and Formulas for Rectangles: Perimeter, Area, and Diagonal Calculation

Rectangle

A rectangle is a quadrilateral with four right angles

A rectangle is a quadrilateral with four right angles. It has opposite sides that are equal in length and parallel to each other. The length and width of a rectangle are its main defining characteristics.

To find the perimeter of a rectangle, you add together the lengths of all four sides. If the length of the rectangle is L and the width is W, then the perimeter P is given by the formula:

P = 2L + 2W

For example, if a rectangle has a length of 5 units and a width of 3 units, the perimeter would be:

P = 2(5) + 2(3)
P = 10 + 6
P = 16 units

To find the area of a rectangle, you multiply the length by the width. The formula for the area A of a rectangle is:

A = L * W

Using the same example of a rectangle with length 5 units and width 3 units, the area would be:

A = 5 * 3
A = 15 square units

It’s important to note that the units used for length, width, perimeter, and area should match. If the length is given in meters, the width should also be in meters, yielding the area and perimeter in square meters and meters respectively.

Additionally, a rectangle has two diagonals that bisect each other at right angles. The length of the diagonal can be calculated using the Pythagorean theorem:

d = √(L^2 + W^2)

Applying this formula to the same rectangle example, we have:

d = √(5^2 + 3^2)
d = √(25 + 9)
d = √34 units

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