The Geometry of Rectangles | Properties, Formulas, and Calculations for Perimeter, Area, and Diagonal

Rectangle

A rectangle is a quadrilateral with four right angles (90-degree angles)

A rectangle is a quadrilateral with four right angles (90-degree angles). It is a two-dimensional shape that has four sides, and opposite sides are parallel and congruent (equal in length). The opposite sides of a rectangle are also perpendicular to each other, meaning they intersect at right angles.

Properties of a rectangle:
1. All angles in a rectangle are right angles (90 degrees).
2. Opposite sides of a rectangle are parallel and congruent in length.
3. Diagonals of a rectangle are congruent and bisect each other.
4. The perimeter of a rectangle can be calculated by adding the lengths of all four sides.
5. The area of a rectangle can be found by multiplying the length and width of the rectangle.

Formulas related to rectangles:
1. Perimeter of a rectangle: P = 2(l + w), where l is the length and w is the width of the rectangle.
2. Area of a rectangle: A = l * w, where l is the length and w is the width of the rectangle.
3. Diagonal of a rectangle: D = √(l^2 + w^2), where l is the length and w is the width of the rectangle.

Example: Let’s say we have a rectangle with a length of 6 units and a width of 4 units.
1. The perimeter of the rectangle would be P = 2(6 + 4) = 2(10) = 20 units.
2. The area of the rectangle would be A = 6 * 4 = 24 square units.
3. The diagonal of the rectangle would be D = √(6^2 + 4^2) = √(36 + 16) = √52 = 2√13 units.

Remember, a rectangle is a specific type of quadrilateral with four right angles, and its properties and formulas can help us calculate various measurements related to it.

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