The Properties and Calculations of Rectangles: Sides, Angles, Diagonals, Area, and Perimeter

Rectangle

A rectangle is a geometric shape that has four sides and four right angles

A rectangle is a geometric shape that has four sides and four right angles. It is characterized by having opposite sides that are equal in length and parallel. The two pairs of opposite sides are also equal in length.

Properties of a Rectangle:

1. Sides: A rectangle has four sides. The opposite sides are equal in length, making it a parallelogram.

2. Angles: The four angles of a rectangle are right angles, meaning they measure exactly 90 degrees each. The sum of all angles in a rectangle is 360 degrees.

3. Diagonals: The diagonals of a rectangle bisect each other at their midpoints, meaning they divide each other into two equal parts. The length of the diagonals can be calculated using the Pythagorean theorem.

4. Area: The area of a rectangle can be calculated by multiplying the length of one side (base) by the length of an adjacent side (height). Area = length x width.

5. Perimeter: The perimeter of a rectangle can be calculated by adding the lengths of all four sides. Perimeter = 2(length + width).

Example:

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

1. Sides: The opposite sides are of equal length, so both pairs of opposite sides will measure 6 units and 4 units respectively.

2. Angles: All angles will measure 90 degrees.

3. Diagonals: The diagonals will be the hypotenuses of two right triangles formed within the rectangle. The Pythagorean theorem can be applied to find their length:

Diagonal^2 = length^2 + width^2
Diagonal^2 = 6^2 + 4^2
Diagonal^2 = 36 + 16
Diagonal^2 = 52
Diagonal ≈ 7.21 units (rounded to two decimal places)

4. Area: The area of the rectangle can be calculated by multiplying the length and width: Area = 6 units x 4 units = 24 square units.

5. Perimeter: The perimeter of the rectangle can be calculated by adding all four sides: Perimeter = 2(6 units + 4 units) = 20 units.

So, in this example, the rectangle has a length of 6 units, a width of 4 units, an area of 24 square units, and a perimeter of 20 units.

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