## rectangle

### In geometry, a rectangle is a quadrilateral with four right angles (90-degree angles) and opposite sides that are equal in length

In geometry, a rectangle is a quadrilateral with four right angles (90-degree angles) and opposite sides that are equal in length. It is a special type of parallelogram, where both pairs of opposite sides are parallel and equal in length.

Properties of a Rectangle:

1. Four right angles: Each angle in a rectangle measures 90 degrees. The sum of the interior angles of a rectangle is always 360 degrees.

2. Opposite sides are parallel: The two pairs of opposite sides in a rectangle are parallel.

3. Opposite sides are equal: The length of the two pairs of opposite sides in a rectangle are equal.

4. Diagonals are congruent: The diagonals of a rectangle bisect each other, meaning they divide each other into two equal parts. The length of the diagonals is equal.

Formulas for a Rectangle:

1. Perimeter: The perimeter of a rectangle is found by adding the lengths of all its four sides. If the length of the rectangle is denoted by L and the width by W, the perimeter is given by: Perimeter = 2L + 2W.

2. Area: The area of a rectangle is calculated by multiplying the length by the width. If L represents the length and W represents the width, the area is given by: Area = L * W.

3. Diagonal length: The length of the diagonal in a rectangle can be found using the Pythagorean theorem. If L represents the length and W represents the width, the diagonal length (D) is given by: D = √(L^2 + W^2).

Example:

Let’s say we have a rectangle with a length of 6 units and a width of 4 units. We can calculate its perimeter and area.

Perimeter = 2L + 2W = 2(6) + 2(4) = 12 + 8 = 20 units.

Area = L * W = 6 * 4 = 24 square units.

So, the perimeter of the rectangle is 20 units and the area is 24 square units.

Remember, rectangles have various practical applications in fields such as architecture, engineering, and mathematics, and understanding their properties and formulas can be useful in solving various geometric problems.

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