A four-side polygon where interior angle \(90^{\circ}\) is called a rectangle. The rectangle like the square is one of the most commonly known quadrilaterals.
It is defined as having all the interior angles \(90^{\circ}\) it is also called the right angle. The two main parts of the rectangle are the vertex is the corner of a rectangle and the perimeter is the total distance covered outside of a rectangle.
What is The Perimeter of a Rectangle?
It is a very common question how to find the perimeter of a rectangle.
Like any polygon, the perimeter is the total distance around the outside which can be found by adding the length of each side.
In the case of a rectangle, the opposite sides are equal in length so the perimeter is twice its width plus twice its height its formula is.
$$P=2(w+h)$$
Where \(P\) is the perimeter \(w\) is the width of the rectangle and \(h\) is the height of the rectangle.
This formula can also be written as well.
$$P=2(l+w)$$
Or
$$P=2l+2w$$
Hare \(l\) is the length or height of the rectangle.
What is The Area of a Rectangle?
How can find the area of a rectangle? The answer to the question is that the area and the number of square units fill a rectangle.
Formula
$$\text{area}=\text{length} \times \text{width}$$
The area of a rectangle is given by multiplying the width times the height or length its formula also is,
$$A=(l \times w)$$
Hare \(A\) is the area of a rectangle \(l\) is the height or length \(w\) is the width of a rectangle.
Length of the Diagonal Rectangle
The diagonal of a rectangle divides a rectangle into two right triangles the diagonals of a rectangle is the hypotenuse of these triangles we can use Pythagoras’ theorem to find the length of the diagonal if we know the height of the rectangle. The formula for the length of the diagonal is.
$$\text{length of diagonal}=\sqrt{w^{2}+h^{2}}$$
Here \(w\) is the width or length and \(h\) in height
Golden Rectangle
A golden rectangle is a type of rectangle whose side lengths are in the golden ratio, which is approximately \(1.618:1\) This ratio is considered aesthetically pleasing and has been used in art, architecture, and design for centuries. In a golden rectangle, if you divide the longer side by the shorter side, you get the golden ratio, also known as phi \(\phi\).
In a golden rectangle, the ratio of the length to the width is
$$\frac{1+\sqrt{5}}{2}a$$
Properties of Rectangle
Opposite sides are parallel and congruent adjust the rectangle above and satisfy yourself that this is so.
The diagonals bisect each other.
The diagonals are congruent
What Is a \(3d\) Rectangle called?
A three-dimensional shape that resembles a rectangle, but extends into the third dimension, is called a rectangular prism or a rectangular cuboid. It’s essentially a box-like structure with six rectangular faces, where opposite faces are equal in size and shape. This shape is commonly encountered in everyday objects such as shoeboxes, building blocks, and some types of packaging. The term “rectangular prism” emphasizes its geometric properties, while “rectangular cuboid” emphasizes its box-like appearance.
Black Rectangle
A “black rectangle” simply refers to a rectangle that is coloured black. It’s a geometric shape with four sides, four right angles, and opposite sides that are equal in length. The term “black” describes the colour of the rectangle, indicating that it appears dark or devoid of light.
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FAQs
What is a rectangle in maths?
A rectangle in mathematics is a quadrilateral with four right angles and opposite sides of equal length.
What is a rectangle formula of area?
The formula for the area of a rectangle is
$$A=l\times w$$
What is a rectangle formula of perimeter?
The formula for the perimeter of a rectangle is
$$p=2(l+w)$$
What is the Definition of a rectangle for class \(1\)?
A rectangle is a shape with four sides, where opposite sides are equal in length and all angles are right angles \(90^{\circ}\)
“If you want to read more about what defines a rectangle and its properties, check out this comprehensive article on ‘What is a Rectangle?‘”
Conclusion
A rectangle is a fundamental geometric shape characterized by four straight sides and four right angles. It falls under the category of quadrilaterals, specifically parallelograms, with unique properties distinguishing it from other shapes. The defining feature of a rectangle is that opposite sides are equal in length and all interior angles measure \(90\) degrees.
This symmetry leads to additional properties such as equal diagonals, which bisect each other, and a constant sum of interior angles.
Rectangles are widely encountered in everyday life, from architectural structures to household items, due to their regularity and efficiency in enclosing space. The formulae for calculating the area and perimeter of rectangles, based on their length and width, are fundamental concepts in mathematics and find practical application across various fields. In essence, rectangles serve as foundational elements in geometry and play a crucial role in both theoretical understanding and practical applications.
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