Understanding Rectangles: Properties, Formulas, and Examples for 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 is characterized by having opposite sides that are equal in length. The length of the longer sides is called the length (l) and the length of the shorter sides is called the width (w).

Properties of a Rectangle:

1. Opposite sides are equal: In a rectangle, the length of the opposite sides is always equal. This implies that the length of one pair of opposite sides is equal to the other pair.

2. Adjacent sides are perpendicular: A rectangle has four right angles. This means that the adjacent sides at each corner meet at a 90-degree angle.

3. Diagonals are congruent: The diagonals of a rectangle bisect each other, meaning they cross at their midpoints. Additionally, the diagonals are congruent in length. This indicates that the length of one diagonal is equal to the length of the other diagonal.

Formulas for a Rectangle:

1. Perimeter (P): The perimeter of a rectangle is equal to the sum of all its side lengths. Therefore, we can calculate the perimeter using the formula:

P = 2(l + w)

2. Area (A): The area of a rectangle is given by the product of its length and width. The formula to calculate the area is:

A = l * w

3. Diagonal (d): The length of the diagonal of a rectangle can be found using the Pythagorean theorem. The formula is:

d = √(l^2 + w^2)

Example:

Let’s consider a rectangle with a length of 6 cm and a width of 4 cm.

1. Perimeter:
P = 2(6 + 4) = 2(10) = 20 cm

2. Area:
A = 6 * 4 = 24 cm^2

3. Diagonal:
d = √(6^2 + 4^2) = √(36 + 16) = √52 = 7.211 cm (approximated to three decimal places)

I hope this helps you understand the concept of a rectangle and its properties, as well as the formulas used to calculate its perimeter, area, and diagonal. If you have any further questions, feel free to ask!

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