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Rectangle: Properties, Perimeter and Area

What is a Rectangle?

A rectangle is a four-sided polygon, known as a quadrilateral, where every angle is a right angle (90 degrees). Unlike squares, the sides of a rectangle do not need to be of equal length; however, opposite sides are always parallel and equal in length. This simple yet versatile shape is omnipresent, from the design of rooms and buildings to various objects we use every day.

Properties of a Rectangle

Understanding a rectangle's properties helps in grasping more complex geometrical concepts. Here are the key properties:

  1. It has four sides, with opposite sides being equal in length.
  2. Each of its angles measures 90 degrees.
  3. The diagonals of a rectangle are equal in length and bisect each other.
  4. The perimeter of a rectangle is the total distance around its edges.
  5. The area of a rectangle is the measure of the space enclosed within its boundaries.

Perimeter of a Rectangle

The perimeter of a rectangle is calculated by adding the lengths of all four sides. Since opposite sides are equal, the formula simplifies to:

Perimeter = 2 * (length + width)

Example

For a rectangle with a length of 10 units and a width of 5 units, the perimeter would be:

Perimeter = 2 * (10 + 5) = 30 units.

Area of a Rectangle

The area of a rectangle is calculated by multiplying the length by the width. This gives the amount of space that is enclosed within the rectangle. The formula is:

Area = length * width

Example

For the same rectangle with a length of 10 units and a width of 5 units, the area would be:

Area = 10 * 5 = 50 square units.

FAQs

What if the Length and Width are the Same?

If the length and width of a rectangle are the same, it becomes a square. The formulas for perimeter and area still apply, but you can simplify the calculations since all four sides are equal.

Can a Rectangle Have Rounded Corners?

No, by definition, a rectangle has straight sides and right angles. A shape with rounded corners would be considered a different type of polygon or shape.

How Do You Find the Diagonal of a Rectangle?

The diagonal of a rectangle can be found using the Pythagorean theorem, which is:

Diagonal = square root of (length^2 + width^2)

This formula gives the length of the diagonal, connecting opposite corners of the rectangle.

Mathematics

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