This area of a rectangle calculator can answer your problem in the blink of an eye, whether you need to know the area of a carpet, a parcel, a TV screen, a rectangular pool, or a window, and you can use this in everyday life! Simply enter the length and width (or diagonal) of the rectangle, and this rectangle calculator will calculate the values of P (perimeter) and A (area) (area).

Continue reading if you want to know what a rectangle is, how to define one, how to use formulae, and what features a rectangle has… Or perhaps you simply want to know how to calculate the area of a rectangle. Also, learn more about rectangular prism with our Surface Area of a Rectangular Prism Calculator.

What is a rectangle? Rectangle definition

In the Euclidean plane geometry, it is mentioned that a rectangle shape is a quadrilateral with four right angles. In the Euclidean plane geometry, it is mentioned that a rectangle shape is a quadrilateral with four right angles. Alternatively, it can be described as an equiangular quadrilateral because all of its angles are equal (360°/4 = 90°), or a parallelogram with those angles. A square is a rectangle with four equal-length sides.

The original word rectangle is actually from the Latin word rectangulus, and this word is from the words rectus (right, right) and angulus (angle).

A crossed rectangle is a quadrilateral with two opposing sides and two diagonals that are self-intersecting (therefore, only two sides are parallel). It’s a type of antiparallelogram with angles that aren’t all right and equal, albeit opposing angles are. Other geometries, such as spherical, elliptic, and hyperbolic, feature so-called rectangles with equal length opposing sides and equal angles that aren’t right.

Many tiling issues use rectangles, such as tiling the plane with rectangles or tiling a rectangle with polygons.

How to find the area of a rectangle?

Finding the area of rectangle is accessible. There are four sides to it, as well as four right angles. The letters a and b are the length of its side, and the letter d is the diagonal size.

A square is a rectangle with equal lengths on all sides. The area of rectangle is the space of its sides. So your job is just to calculate the rectangle’s area by multiplying the rectangular sides a and b.

Area={a}\cdot{b}

Rectangle formulas

We have more formulas for rectangles. Those formulas are:

  • For a rectangle’s area, use the following formula:
A={a}\cdot{b}
  • For a rectangle’s perimeter, use the following formula:
P=2\cdot(a+b)
  • In the case of a rectangle’s diagonal:
d^2=a^2+b^2

The surface area of a rectangle

The length of any two contacting sides multiplied together equals the area of a rectangle. To put it another way, length multiplied by breadth.

We have a couple of ways to find the surface area of a rectangle, but to find out, keep reading. These ways are:

  • Your rectangular prism’s length, width, and height should all be labeled. There are three dimensions to each rectangular prism: length, width, and height. Make a diagram of the prism and draw the letters l, w, and h next to three distinct edges. Pick any corner if you’re not sure which sides to designate. The three lines that intersect at the corner should be labeled. Consider the following scenario: The base of a box is 3 inches by 4 inches, and it stands 5 inches tall. The base’s long side is 4 inches long, thus l = 4, w = 3, and h = 5.
  • Examine the prism’s six faces. Six separate “faces” would be required to cover the whole surface area.
  • Locate the lower face’s area. To begin, calculate the surface area of only one face: the bottom. This, like every other face, is a rectangle. The length of one edge of the rectangle is labeled, while the width of the other is indicated. Simply multiply the two edges together to determine the rectangle’s area. lw = length times width Equals area (bottom edge).

Returning to our example, the bottom face has a surface area of 4 inches by 3 inches, or 12 square inches.

  • Locate the upper face’s area. Wait a minute – we’ve already seen that the top and bottom faces are identical in size.
  • Determine the front and rear facial areas. Return to your diagram and examine the front face, the one with one width edge and one height edge. The breadth times the height of the front face equals wh. The back region is likewise whitish.
  • Determine the area of the faces on the left and right. We only have two faces remaining, both of which are the same size. One edge represents the prism’s length, while the other is the prism’s height. The left face’s region is lh, and the right face’s area is also lh.
  • Combine the six sections. You’ve now determined the surface area of each of the six faces.

Rectangle example 1: find A (area of a rectangle)

We’ll give an example to show how to apply the formula to calculate area of a rectangle. Example is:

  1. Choose the rectangle’s length, for example, a = 4 cm.
  2. Decide on the rectangle’s width, for example, b = 3 cm.
  3. Multiply these two numbers to get 12cm2: A = 4 cm x 3 cm.

The rectangle has a surface area of 12 cm2.

Rectangle example 2: find P (perimeter of a rectangle)

Let’s see how to calculate perimeter of a rectangle. By adding all its pages we get a range of shapes:

P=a+b+a+b

Which we also write like:

P=2\cdot(a+b)

As an example, consider the following rectangle:

  1. Choose the rectangle’s length – in our example, a = 4 cm.
  2. Decide on the rectangle’s width, for example, b = 3cm.
  3. Add these two numbers together: a + b = 4 + 3 = 7 cm.
  4. P = 2 x 7 = 14 cm, is the result of multiplying the result by two.

Our rectangle has a 14-cm perimeter.

Rectangle example 3: find D (diagonal of a rectangle)

A rectangle’s diagonal is a line segment that links two of the rectangle’s opposing vertices. Let’s see how to figure out the diagonal length of the illustrative rectangle:

  1. Choose the rectangle’s length, for example, a = 4cm.
  2. Decide on the rectangle’s width, for example, b = 3 cm.
  3. Calculate a to the power of two: a² = 16 cm².
  4. Calculate b to the power of two: d = √(a² + b²) = √25 ~ 5 cm.
  5. These two numbers are added together: a² + b² = 16 + 9 = 25 cm².
  6. Finally, take the result’s square root: d = √(a² + b²) = √25 ~ 5 cm.

The diagonal measures 5 cm in length.

Golden rectangle

This is a specific type of rectangle. Certain requirements must be met by such a rectangle, and these requirements are as follows:

\frac{(a+b)}{a}=\frac{a}{b}= φ

where φ is the golden ratio equal to 1.618.

What is the ratio?

The connection between two quantities, commonly expressed as a fraction, is called a ratio.

Did you know that all you need is a straightedge and a compass to make the golden triangle? It only takes a few steps! The steps are:

  1. make a square with your pencil,
  2. draw a line going from one corner of the square to the opposite corner on one side,
  3. as shown in the example, draw a circle with a radius equal to that line and a center at the midway,
  4. the next corner of the golden rectangle is the point where the circle meets the expanded square side, and
  5. complete the golden rectangle by finding the last vertex.

Properties of a rectangle

Rectangles offer a lot of fascinating characteristics. A rectangle consists of the following elements:

  1. is cyclic, which means that all of its corners are contained within a single circle,
  2. is equiangular, meaning that all of its corner angles are 90 degrees,
  3. Its sides meet at right angles, making it rectilinear,
  4. through the center, there are two lines of reflectional symmetry: vertical and horizontal,
  5. there are two diagonals that cross each other. The Pythagorean theorem may be used to calculate the diagonal length,
  6. a rectangle’s opposite sides are parallel to one other and have the same length.

Other rectangular qualities that are less well-known include:

  1. The circumcenter is the location where the diagonals connect; a circle with a center in that point and passing through the four corners exists.
  2. It is impossible to draw the incircle in a rectangle with varied side lengths (simply speaking – not a square).
  3. A rhombus is formed by connecting the midpoints of the sides of a rectangle, which is half the area of the rectangle. The diagonals are parallel to the sides of the form.

You may also consider your own attributes, such as the rotation of a rectangle along the side or diagonal to obtain a cylinder or a cone, respectively.

Rectangle patterns

Many periodic tessellation patterns employ the geometry of a rectangle. It may be useful for brick walls, floor tiles, pavement, and other mosaics. A few common designs are below:

  1. stacked bond is the most popular and simplest tiling design and has tiles in straight lines,
  2. running bond is a type of bond that we use for pavements and brick bonding,
  3. herringbone – this type of design looks great on hardwood flooring and
  4. basketweave is a popular choice for corridors and outdoor walkways.

Tiles are available in a wide range of sizes and forms, with hexagonal and octagonal squares being popular choices. To create a tiling pattern, the pentagon’s shape must be uneven.

FAQ

What are the vertices of a rectangle

All internal angles are 90° in a quadrilateral, and the coordinates of the four vertices establish its placement on the coordinate plane (corners).
The coordinates of a rectangle’s four vertices are (3, 4), (0, 4), (0, -1), and (2, -1).

How to find the maximum area of a rectangle

The disparity in length and width must be minimum for any rectangle’s area to be maximized. As a result, the length should be ceil (perimeter / 4) and the width should be floor (perimeter /4). As a result, ceil(perimeter/4) * floor(perimeter/4) equals the greatest area of a rectangle with a given perimeter.

How to measure the area of a rectangle

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

What is the area and perimeter of a rectangle

The perimeter of a rectangle is calculated using the formula P=2l+2w, where l is the rectangle’s length and w is its width. The formula A=lw gives the area A of a rectangle, where l is the length and w is the width.

Are diagonals of a rectangle perpendicular

The diagonals in the rectangle are equal. And it’s important to mention that they split in half. The diagonals in a diamond are perpendicular to each other. All of these are true in a square. The diagonals are perpendicular to each other, equal to each other, and bisect each other.