# How to find the area of a rectangle using the diagonal

Calculating a square area is as easy as multiplying the length by the width. But when you have a curved surface like a sphere or a cylinder, the problem can be puzzling. Luckily, mathematicians have figured out formulas for curved surfaces, so all you have to do is take a couple of simple measurements and plug the measurements into the formulas. For example, if you know the radius of a sphere, you can use the formula 4 pi r^2 to calculate its surface area. The surface area of a cylinder can be calculated with the height and radius using the formula 2 pi r^2 + 2 pi r h.

## Surface Area of a Sphere

Square the radius. For example, if the radius is 5 inches, then: 5 inches * 5 inches = 25 inches squared.

Multiply Step 1 by pi. Pi * 25 inches squared = 78.54 inches squared.

Multiply Step 2 by 4: 78.54 inches squared * 4 = 314.16 inches squared.

## Cylinder

Square the radius. For example, if the radius is 2 inches, then: 2 inches * 2 inches = 4 inches squared.

Multiply Step 1 by 6.28. 6.28 * 4 inches = 25.04 inches.

Multiply the radius by the height. For example, a radius of 2 inches and a height of 10 inches would give you: 2 inches * 10 inches = 20 inches squared.

Multiply Step 3 by 6.28: 20 inches squared * 6.28 = 125.6 inches squared.

Add Step 2 and Step 4 together: 25.04 inches squared + 125.6 inches squared = 150.64 inches.

Although 3.14 is a good approximation of pi and will work for most calculations, you can increase the accuracy of your answers by adding more decimal places to pi. For example, use 3.1416 for pi (4 decimal places) and 6.2832 for 2pi.

Our diagonal of a rectangle calculator is an extensive tool that quickly finds the diagonal and other parameters of a rectangle. Have you met a specific rectangle problem and you don't know how to find the diagonal of a rectangle? Try entering a couple of parameters in the fields beside the text or keep reading to find out what are the possible diagonal of a rectangle formulas.

You can see a typical rectangle in the figure below. We have marked five basic quantities that describe a specific rectangle. You can use them to derive the diagonal of a rectangle formula. These are:

• l – length,
• w – width,
• α – angle between diagonals,
• d – diagonal,

and two other parameters which are not shown in the picture:

• A – area,
• P – perimeter.

The term rectangle comes from the Latin rectangulus that is a combination of two words: rectus (right, proper) and angulus (angle). This name derives from the fact that a rectangle is a quadrilateral with four right angles (4 * 90° = 360°). Its opposite sides are parallel and of equal length, and its two diagonals intersect each other in the middle and are of equal lengths too.

A square is a special case of a rectangle. Its definition is that it has all four sides of equal length, or alternatively, the angle between two diagonals is right. Go ahead on try our calculators dedicated to squares. They can quickly estimate the perimeter, area and diagonal of every square you want, just from the length of its side.

The center of a rectangle is equidistant from its vertices, and therefore you can always circumscribe a circle on it. On the other hand, you can inscribe a circle into a rectangle only if it is a square.

## How to find the diagonal of a rectangle?

To find the diagonal of a rectangle formula, you can divide a rectangle into two congruent right triangles, i.e., triangles with one angle of 90°. Each triangle will have sides of length l and w and a hypotenuse of length d . You can use the Pythagorean theorem to estimate the diagonal of a rectangle, which can be expressed with the following formula:

and now you should know how to find the diagonal of a rectangle explicit formula – just take a square root:

Our diagonal of a rectangle calculator allows you to use almost any units you want. Check out our length converter or area converter to find out how to switch between different units (SI and imperial).

## What's the diagonal of a rectangle formula?

Sometimes you won't have given all of two rectangle's sides. How to find the diagonal of a rectangle in that situation? The answer is provided with our diagonal of a rectangle calculator. At first, let's write down three basic equations, for the area, perimeter and circumcircle radius:

1. Area of a rectangle: A = w * l ,
2. Perimeter of a rectangle P = 2 * w + 2 * l ,
3. Circumcircle radius of a rectangle r = d/2 .

With the above equations, we can now derive various diagonal of a rectangle formulas that are used by this diagonal of a rectangle calculator:

1. Given length and width: d = √(l² + w²) ,
2. Given length/width and area: d = √(A²/l² + l²) or d = √(A²/w² + w²) ,
3. Given lenght/width and perimeter: d = √(2l² – P*l + P²/4)) or d = √(2w² – P*w + P²/4) ,
4. Given length/width and angle: d = w / sin(α/2) or d = l / cos(α/2) ,
5. Given area and perimeter: d = √(P² – 2*A) ,
6. Given area and angle: d = √(2 * A / sin(α)) ,
7. Given perimeter and angle: d = P / (2*sin(α/2) + 2*cos(α/2)) ,
8. Given circumcircle radius: d = 2 * r .

Note: The angle α between diagonals is in the front of the length like in the first figure. Also, remember that the diagonal of a rectangle calculator assumes that the length is longer than the width!

Did you know that there is a special rectangle called the golden rectangle? If not, head on to our golden rectangle calculator and see how you can construct golden rectangles!

Topic:

Example:
We make a straight legged arch, This shape has a width a overall height and a leg height, The leg height is always less then the overall, And the top is arched. We have the width, Height, and leg size.

Lets say I have a triangle,

Not any ordinary triangle, but a triangle that is represented in 3 dimensions. I also have a line segment.

Lets say that this triangle has points A(0,0,0), B(1,0,0), C(0,1,1)

And the line segment has points D(0,1/2,0), E(1,1/2,1)

In what way can I find if the line segment and triangle intersect? Their intersection point?

I don’t prefer matrices, because they don’t make any sense, but . if that’s the only way to solve this, then do what’s necessary.

I was previously to be purchasing a square 1 acre plot, which I believe was to have 209feet, 4 sides perimeter.

b)Pass a plane through a cube of edge 8 in so that the section formed will be a regular hexagon. Through each side of the hexagon pass two planes, one plane containing one of the two vertices of the cube which are farthest away from the plane of the hexagon, the other plane containing the diagonally opposite vertex of the cube. Find the volume of the solid bounded by these planes.

c)three of the edges of a rectangular parallelepiped that meet in a point are also the lateral edges of a pyramid. What fraction of the parallelepiped is this pyramid.

Empirically I can figure out that 3 x 3 x 3 equals 27 and that 3.5 feet (42″) x 3.5 x 3.5 equals 42.87 and 3.75 x 3.75 x 3.75 equals 52.73 which is about 1.5 cubic meters (1cubic meter = 52.971643 cubic feet) i.e a box 45 x 45x 45 “

I would like to know the equation to use to find the inside dimensions of a box if I know how many cubic feet (or inches) I need the inside to be.

The 300-metre tall Eiffel tower is made of steel and weighs 8 000 000 kg. An exact replica, made of the same material, weighs 1 kg. How high is the replica

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.

Is it possible to find the width and length of a rectangle by just know the diagonal? Like if the diagonal was 25, what would be the side lengths?

Any help is appreciated!

EDIT: From the comments and solutions this is not possible. Thanks for the explanations!

Say your diagonal was length $c$ , and it’s width and height was $a$ and $b$ respectively, then these must satisfy

This has many solutions for $a$ and $b$ given the diagonal $c$ .

No. By Pythagoras, if the width is $a$ and the length $b$ , then,

Any pair of numbers that satisfies that equation is a possible rectangle for that diagonal. For example, $a=15, b=20$ , or $a=125/13, b=300/13$ , etc.

It is not enough to just know the length of the diagonal. But there are different additional hints that can make it possible.

• if the rectangle is a square the side $a=d/\sqrt2$
• if the ratio between the sides $r=a/b$ is known $b=\sqrt<\frac>$
• if the angle $\alpha$ between the diagonals is known $a=d\cdot sin(\frac<\alpha><2>)$

Those are some but not all possible hints that can help.

Another approach. If you know the side of a triangle and the opposite angle, the possible locations of the vertex which isn’t on the original side lie on an arc of a circle of known radius. With a right-angle the side you have is a diameter of the circle. The diagonal splits the rectangle into two triangles.

This is a lesser known consequence of the sine rule $$\frac a<\sin A>=2R$$ where $R$ is the radius of the circumcircle of the triangle.

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Welcome to the rectangle area calculator. When we look around us, we find that the majority of items in our daily life are rectangular in shape. Even the laptop or mobile that you are using to read this post is rectangular. It means, we interact with a lot of rectangles in our daily routine without noticing it.

By using area of rectangular calculator, the following terms can be calculated:

• Area of rectangle
• Length
• Width
• Diagonal
• Perimeter

You may need to calculate the area of your room for furnishing or the area of carpet to lay it in one of your guest rooms. The rectangle calculator lets you calculate the area of any rectangle that can pop up into your mind.

Even if you need to find the perimeter of your lawn to install a fence around it, this tool will help you measure the surroundings of your lawn. What? Your lawn is not rectangular? Don’t worry. In case, you have a circular lawn or playground, you can still measure it by using our circumference calculator.

In this article, we are going to discuss how to use rectangular area calculator, rectangular definition, formula for rectangle area, and how to can you find area of rectangle.

## How rectangle area calculator works?

Area of a rectangle calculator efficiently computes the rectangle area as well as perimeter, sides, and diagonal. It is accurate and robust tool which makes the whole process of calculation effortless. To use this calculator, follow the below steps:

• Choose the option to solve for. i.e., area, perimeter, etc.
• Select the given set of parameters form the list.
• Enter the required values in the given input boxes.
• Hit the Calculate button to get the instant result.

It will show you the calculated area, the formula it used for calculation, and all steps that are involved in the calculation.

Rectangle is a type of quadrilateral. If you want to calculate the area of any other quadrilateral, you can use our trapezoid area calculator, rhombus area calculator, or kite area calculator anytime.

## What is a rectangle?

A rectangle is a quadrilateral having 4 straight sides and 4 angles of 90°. All opposite sides are equal and parallel to each other.

In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°). It can also be defined as a parallelogram containing a right angle.

## Properties of a Rectangle

Properties of a rectangle are given below:

• All angles are right angles.
• Opposite sides are congruent and parallel.
• A rectangle is a special type of parallelogram whose angles are right.
• The diagonals are bisect each other and congruent.
• Opposite angles formed at the point where diagonals meet are congruent.

## Rectangle area formula

Formula for area of a rectangle is much simpler than you think. It can be stated as:

Area of a rectangle = a × b

a is the length of the rectangle,

b is the width of the rectangle.

### Perimeter of a rectangle formula

The formula for perimeter of rectangle can be stated as:

a is the length of the rectangle, and b is the width of the rectangle.

### Diagonal of a rectangle formula

The formula for diagonal of rectangle can be stated as:

a is the length of the rectangle, and b is the width of the rectangle.

## How to calculate area of a rectangle?

Now that you know how to find the area of a rectangle, let’s take a deep dive into the manual rectangle area calculation. To find the area of a rectangle, you should have the length and width of the rectangle. If you do not, measure your rectangle using a measuring tape.

Follow the below steps to calculate rectangle area

• Write down the length and width of the rectangle.
• Write down the formula of area of rectangle.
• Substitute the values in the formula and calculate the area.

Find the area of a rectangle having length of 20 cm and width of 8 cm?

Step 1: Write down the length and width of the rectangle.

a = 20 cm, b = 8 cm

Step 2: Write down the formula of area of rectangle.

Area of a rectangle = a × b

Step 3: Substitute the values in the formula and calculate the area.

Area = 20 cm × 8 cm

So, the area of a rectangle with length of 20 cm and width of 8 cm is 160 cm 2 .

### Area of rectangle – Real world example

If the area of a rectangular room is 150 square feet, and its width is 10 square feet, what will be the length of that room?

Step 1: Write down the area and width of the room.

Area = 150 sq. feet, b = 10 sq. feet

Step 2: Write down the formula of area of rectangle.

Area of a rectangle = a × b

Step 3: Substitute the values in the formula and calculate the length of the room.

Length (a) = 150/10 = 15 feet

So, the length of a rectangular room having area of 150 sq. feet and width of 10 sq. feet is 15 feet.

### What is the formula of rectangular area?

The formula of rectangular area is:

Rectangular area = length × width

### How do you calculate total area of rectangle?

The total area of rectangle can be calculated by multiplying its length and width. The multiplication of length and width of a rectangle gives the total area of a rectangle.

Total area of rectangle = length × width

### How do you find the sides of a rectangle given the area?

A side of the rectangle can be calculated if area and one side is given. It can be calculated by using the same formula that we use to calculate its area. Area = length × width.

Suppose we have rectangle with 8 cm length and its area is 24 cm 2 . We can calculate its width by substituting the values in the above equation.

24 cm 2 = 8 cm × width

Width = 24/8 = 3 cm

### How do you find the length and area of a rectangle?

The area of a rectangle can be calculated by this equation:

Area = length × width

While length of a rectangle can be calculated by rearranging the above equation:

Length = Area / Width

The online jsBeautifier is a free online program that is worth bookmarking.

Write a Python Program to find Area of a Rectangle and Perimeter of a Rectangle with example. Before we step into the Python Program to find Area of a Rectangle example, Let see the definitions and formulas.

## Python Area of a Rectangle

If we know the width and height then, we can calculate the area of a rectangle using below formula.

Area = Width * Height

Perimeter is the distance around the edges. We can calculate perimeter of a rectangle using below formula

Perimeter = 2 * (Width + Height)

### Python Program to find Area of a Rectangle and Perimeter of a Rectangle

This program for Area of a rectangle allows the user to enter width and height of the rectangle. Using those values, this python program will calculate the Area of a rectangle and perimeter of a rectangle.

Following statements will allow the User to enter the Width and Height of a rectangle.

Next, we are calculating the area as per the formula

In the next Python line, We are calculating the Perimeter of a rectangle

Following print statements will help us to print the Perimeter and Area of a rectangle

### Python Program to find Area of a Rectangle using functions

This Python area of rectangle program allows the user to enter the width and height of a rectangle. We will pass those values to the function arguments to calculate the area of a rectangle.

Within this area of rectangle program, First, We defined the function with two arguments using def keyword. It means, User will enter the width and height of a rectangle. Next, We are Calculating the perimeter and Area of a rectangle as we described in our first example.

## Python Program to find Area of a Rectangle and Perimeter of a Rectangle

• This program allows the user to enter width and height of the rectangle. Using those values we will calculate the Area of a rectangle and perimeter of a rectangle.

## Output

Learn Python – Python tutorial – Python Program to find Area of a Rectangle and Perimeter of a Rectangle – Python examples – Python programs

## Analysis

• Following statements will allow the User to enter the Width and Height of a rectangle.
###### click below button to copy the code. By Python tutorial team
• Next, we are calculating the area as per the formula
###### click below button to copy the code. By Python tutorial team
• In the next line, We are calculating the Perimeter of a rectangle
###### click below button to copy the code. By Python tutorial team
• Following print statements will help us to print the Perimeter and Area of a rectangle

## Python Program to find Area of a Rectangle using functions

• This program allows the user to enter the width and height of a rectangle.
• We will pass those values to the function arguments to calculate the area of a rectangle.

## Analysis

• First, We defined the function with two arguments using def keyword.
• It means, User will enter the width and height of a rectangle.
• Next, We are Calculating the perimeter and Area of a rectangle as we described in our first example.

## Output

Learn Python – Python tutorial – Python Program to find Area of a Rectangle using functions – Python examples – Python programs

NOTE: We can call the function with arguments in .py file directly or else we can call it from the python shell. Please don’t forget the function arguments

Java program to calculate the area of a rectangle. There are maybe so many methods in order to write the java program to find the area of a rectangle. Here we share the two methods, sample method -1, and sample method-2 with online compiler and execution tool.

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Below are the online compiler and execution tool check it out #area of rectangle

what is a rectangle? ( Lol :-p you knew it, but just a couple of lines )

The rectangle is a plane figure with four straight sides or just four right angles.

What is the formula for the area of a rectangle?

The area of a rectangle formula is :

Length X Breadth. Or Length X Width

Here goes the sample program to find or to calculate the area of a rectangle.

Output :

Here is the online execution tool!

The above program is just a simple one. since there may be several ways to represent the program. If you good at basic skills of java programming, just skip the below code explanation part and move on to the sample method-2. Where you can execute the program there by itself. Consider it has another sample method-2.

– Syntax, which read the input values, in simple words, it’s an inbuilt package.

2)

– A class is a blueprint, where objects are created.

3)

– And, the program starts executing from here, the main head of the block program starts here.

4)

– scanner, which reads the input values, and system.in uses to retrieve the data from the JDK package from your system or device.

5)

– Displays, whatever you were written on that syntax, followed by second.

6)

– Double, A memory space where the user can give the values either in decimal points or without decimal points. Since we are using the ” Double “. Double can store the values up to 8 bytes, and the name os the memory is L. Consider it has same to ” B “.

7)

– The formula to find out the area of the rectangle.

8)

– Output displayed here.

We always make sure to write the java program in a simple way to the users and newbies can able to understand the program better. Lengthy codes are way better too, but those extra couple of code lines are actually not necessary.

Here is another simple method to find out the area of a rectangle, the below program is quite simple.

# Sample Method – 2 #

Note: The following program is just for a subject purpose, with your own inbuilt variables directly dumping into the program. That means a user is not required to submit the input values. Just for a subject purpose.