A rectangle has many names but comes from the Latin word rectangulus which means right and straight (rectus) and an angle (angulus). Simply put, it’s a shape with four right angles – a quadrilateral.
You can also define a rectangle as a parallelogram with a right angle. It’s also similar to a square (and technically is one) but has two longer sides sitting parallel to each other.
We will cover the most important question first: how do you find the area of a rectangle? Below, we’ll explain the formula and the shape.
A rectangle has four sides and four right angles. We will give all corners labels A, B, C, and D. We will also identify the diagonal point through point B to C with a small d.
To find the area of a rectangle, you multiply the A side by the B side. The formula looks like this:
Area = A x B
Even though you can use this calculator to work out the area of a rectangle, you can also use it for perimeters and the diagonal of a rectangle. The formulas for these are below.
Perimeter = 2 x (A + B)
Diagonal = d² = a² + b²
Above, you discovered that the area of a rectangle’s formula is A x B. An example of this formula in action is below.
1. Identify the length (B) and width (A). For this example, the length is eight inches, and the width is 15 inches.
2. Multiple the two values.
8 x 15 = 120 inches
The formula for working out the perimeter of a rectangle is:
P = 2 x (A + B)
Or, expanded to: P = A + B + A + B
Using the same dimensions in the previous rectangle (eight-inch length, 15-inch width), you can work out the perimeter of it below.
1. Identify the rectangle’s length
8 inches (b)
2. Identify the rectangle’s width
15 inches (a)
3. Add the values together
a + b = 8 + 15 = 23
4. Multiply that result (23) by two
Perimeter = 2 x 23 = 46
The rectangle’s perimeter is 46 inches.
You can define the diagonal in a rectangle as the piece that connects two vertices in a rectangle that sit opposite each other. Using the same rectangle dimensions as previous examples, (eight-inch length, 15-inch width), we will work out the diagonal of a rectangle.
1. Identify the rectangle’s length
8 inches (b)
2. Identify the rectangle’s width
15 inches (a)
3. To the power of two, calculate a
a² = 225 inches²
4. To the power of two, calculate b
b² = 64 inches²
5. Add the values together
a² + b² = 225 + 64 = 289 inches²
6. Square root the result
d = √ (a² + b²) = √289 ~ 17 inches
The diagonal’s length is 17 inches.
The formula for working out such a rectangle is:
(a + b) / a = a / b = ϕ
ϕ (Golden Ratio) = 1.618
The ratio refers to the two quantities’ relationship, generally shown as a fraction.
If you are looking to have a bit of fun with a ruler and compass, you can build a golden rectangle for yourself in only five steps!
1. Draw a square
2. Form a line from one side of the square’s midpoint to the opposite corner
3. Create a circle with its radius sitting equal to the line with its center in the midpoint
4. Identify the meeting point of the circle and the square to form the next corner of the golden rectangle
5. Discover the final vertex to complete the rectangle
You might see a rectangle as a rectangle and nothing more, but there are many interesting facts surrounding the rectangle!
It:
• Is cyclic – all corners are on a circle
• Is equiangular – its corner angles are 90 degrees
• Has two reflectional symmetry lines
• Has parallel and equal length opposite sides
• Is rectilinear with the sides meeting at right angles
• Has bisecting diagonals
You know rectangle by its most common name, rectangle, but when someone refers to it as something else, confusion occurs.
To clear up any misconceptions, you can refer to a rectangle as a parallelogram, a trapezoid, and a quadrilateral. However, a rectangle is not a rhombus because the angles of a rhombus are not all 90 degrees.
A square is a special kind of rectangle, and every rectangle is a parallelogram. A rectangle is also a special kind of trapezoid.
Australian geo-statistician David Barry was a little curious. The world’s countries are all different shapes and sizes, but which one was the most likely to be rectangular? He set about calculating the shapes of every country in the world to see which one had the most rectangular-like parameters of them all.
And, the winner is…
Egypt.
A perfect rectangle has an index of 1, and Egypt’s roundness was 0.955
You can see who came in second, third, fourth, etc., here.
Once you start thinking about rectangles, you will see they appear in everyday life. They appear as bricks in walls, tessellation patterns, floor tiles, and more. There is even a brick calculator to work out how many rectangular blocks you will need in construction. They form different shapes and patterns, such as these below:
Basketweave: commonplace in outdoor pathways
Stacked: Straight-line stacking style
Running: Most common for brick bonding and pavements
Herringbone: Suitable for wooden flooring
While many people will use a rectangle calculator to solve their math problems, you may be surprised to know it will come in handy for everyday life. That’s because there are far more rectangular objects around you than you think.
You can find out the size of your rectangle table so you can choose the right tablecloth, or you can work out the glass area of your window that you might need to replace. You can use the rectangle calculator to establish how much glass you will need, but you can also use a square-foot calculator if the damage is more far-reaching than you thought.
Even when it comes to working out your screen sizes, a rectangle calculator can come in handy. As you will now realize, when it comes to rectangles and rectangular calculations, the sky’s the limit. What’s more, there’s a calculator for everything!
