Understanding Rectangles: Properties, Area, Perimeter, and Diagonals

Rectangle

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

A rectangle is a shape that has four sides and four right angles. It is a quadrilateral with opposite sides that are equal in length and opposite angles that are equal in measure. In a rectangle, the opposite sides are parallel to each other.

Properties of a Rectangle:
1. Sides: A rectangle has four sides. The two pairs of opposite sides are equal in length. The length of the longer pair of opposite sides is called the length of the rectangle (l), and the length of the shorter pair is called the width of the rectangle (w).
2. Angles: All four angles of a rectangle are right angles, which are equal to 90 degrees. The opposite angles are congruent (equal).

Area of a Rectangle:
The area of a rectangle is the measure of the region enclosed by its sides. The formula to calculate the area of a rectangle is:

Area = length × width or A = l × w

For example, if the length of a rectangle is 5 units and the width is 3 units, then the area would be:

Area = 5 × 3 = 15 square units

Perimeter of a Rectangle:
The perimeter of a rectangle is the total distance around the rectangle. It is calculated by adding up the lengths of all four sides. The formula to calculate the perimeter of a rectangle is:

Perimeter = 2 × (length + width) or P = 2(l + w)

Using the same example as above, where the length of the rectangle is 5 units and the width is 3 units, the perimeter would be:

Perimeter = 2 × (5 + 3) = 2 × 8 = 16 units

Diagonals of a Rectangle:
A rectangle has two diagonals, which are line segments connecting opposite vertices. The diagonals of a rectangle are congruent (equal in measure) and bisect each other, meaning they divide each other into two equal halves.

Using the example of the rectangle with length 5 units and width 3 units, we can calculate the length of the diagonal using the Pythagorean Theorem:

d^2 = l^2 + w^2
d^2 = 5^2 + 3^2
d^2 = 25 + 9
d^2 = 34
d ≈ √34

So, the approximate length of the diagonal is √34 units.

These are some of the main concepts and formulas related to rectangles. If you have any specific questions or need further clarification, please let me know!

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