Ultimate Guide to Rectangles: Properties, Formulas, and Examples

Rectangle

A rectangle is a type of quadrilateral with four sides and four right angles

A rectangle is a type of quadrilateral with four sides and four right angles. It is characterized by opposite sides that are equal in length and parallel to each other. The opposite sides of a rectangle have the same length, which makes its shape symmetrical.

Properties of a Rectangle:
1. Opposite sides are parallel: In a rectangle, the pairs of opposite sides are always parallel to each other. This property allows for the interior angles to be congruent, specifically the opposite interior angles are equal.

2. All interior angles are right angles: A rectangle has four right angles, which means each angle measures 90 degrees. The sum of all the interior angles of a rectangle is 360 degrees.

3. Diagonals are congruent: The diagonals of a rectangle are equal in length. Furthermore, they bisect each other, meaning that they intersect at their midpoints. The diagonals also divide the rectangle into four congruent right triangles.

4. Perimeter formula: The perimeter of a rectangle is calculated by adding the lengths of all four sides. If the length of the rectangle is denoted as “l” and the width as “w”, then the perimeter formula is given by 2(l+w).

5. Area formula: The area of a rectangle is determined by multiplying its length and width. The formula for the area of a rectangle is given by A = l * w, where “A” represents the area, “l” represents the length, and “w” represents the width.

Example:
Consider a rectangle with a length of 6 units and a width of 4 units.
– Opposite sides are parallel: The top and bottom sides are parallel, as well as the left and right sides.
– All interior angles are right angles: All four angles measure 90 degrees.
– Diagonals are congruent: The diagonal divides the rectangle into two congruent right triangles, each with a hypotenuse of length 5. Therefore, the diagonal measures 5 units.
– Perimeter: The perimeter is calculated by adding the lengths of all four sides, which gives 2(6+4) = 20 units.
– Area: The area is obtained by multiplying the length and width, giving 6 * 4 = 24 square units.

I hope this explanation helps you understand the properties and formulas related to rectangles. If you have any further questions or need assistance with specific problems, feel free to ask!

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