How To Find The Dimensions Of A Rectangle

Surface area & Perimeter of a Rectangle calculator uses length and width of a rectangle, and calculates the perimeter, surface area and diagonal length of the rectangle. It is an online Geometry tool requires two length sides of a rectangle. Using this reckoner, we will understand the algorithm of how to find the perimeter, area and diagonal length of a rectangle.
It is necessary to follow the side by side steps:

Enter the length and width of a rectangle in the box. These values must exist positive real numbers or parameter. Notation that the length of a segment is always positive;
Printing the "GENERATE Piece of work" button to make the ciphering;
Rectangle calculator will requite the perimeter, surface area and diagonal length of a rectangle.

Input : Two positive real numbers or parameters as the length and width of a rectangle;
Output : Iii positive existent numbers or variables as the perimeter, area and diagonal length of a rectangle and corresponding units after that.

Rectangle shape

Rectangle Formula :

Perimeter of Rectangle Formula: The perimeter of a rectangle is determined past the following formula

$$P=two\times a+2\times b=2\times(a+b)$$

where $a$ and $b$ are the length and width of the rectangle, respectively.

Area of Rectangle Formula: The expanse of a rectangle is adamant by the following formula

$$A=a\times b$$

where $a$ and $b$ are the length and width of the rectangle, respectively.

Length of Diagonal of Rectangle Formula: The diagonal of a rectangle is determined by the post-obit formula

$$d=\sqrt{a^2+b^2}$$

where $a$ and $b$ are the length and width of the rectangle, respectively.

What is Area & Perimeter of Rectangle?

A quadrilateral with four congruent angles is a rectangle. The give-and-take "rectangle" comes from Latin "rectangulus". It's a combination of "rectus" which ways "right" and "angulus" which means "an angle".
If $\angle A\cong\angle B\cong\angle C\cong\bending D$, then ${\overline{ABCD}}$ is a rectangle (see the moving picture below). It holds that

$$1000\bending A=grand\angle B=m\angle C=one thousand\angle D=\frac{{360}^o}{four}={90}^o$$

The lengths of its sides are denoted by $a$ and $b$, while the length of the diagonal is denoted with $d$. A rectangle is likewise called an equiangular quadrilateral, since all of its angles are congruent.
A rectangle is a parallelogram, simply parallelogram is not a rectangle because in a rectangle each bending is a right angle, whereas it is non so in a parallelogram. That means that all the properties of a parallelogram can be also applied to rectangles. To remember, the parallelogram has the following properties:

Opposite sides of a parallelogram are congruent;
Opposite angles of a parallelogram are congruent;
The consecutive angles of a parallelogram are supplementary to each other;
The diagonals of a parallelogram bisect each other

Rectangle satisfies one more property:

The diagonals of a rectangle are coinciding;

If nosotros know side lengths of the rectangle, it is easy to calculate the length of the diagonal using the Pythagorean Theorem. A diagonal divides a rectangle into ii right triangles. By applying the Pythagorean Theorem to $\Delta ABC$, we get

$$d^ii={\overline{AB}}^two+{\overline{BC}}^2=a^2+b^2$$

i.e.

$$d=\sqrt{a^two+b^ii}$$

The rectangle has only two lines of symmetry. These lines are these ones which connect the midpoints of the opposite sides of the rectangle. A rectangle has primal symmetry and rotational symmetry. The center of symmetry is the point of intersection of its diagonals, $O$.

Rectangle diagonals intersection

The distance around a rectangle is called the perimeter of the rectangle. Information technology is usually denoted by $P$. To notice the perimeter of rectangle we add the lengths of its sides. Thus, the perimeter of a rectangle with the length of $a$ and the width of $b$ is

$$P =a+b+a+b= 2 \times a+ii\times b=2\times(a+b)$$

Perimeter of Rectangle Area of Rectangle

The area of a rectangle or another polygon is a number of square units needed to fill the rectangle. The area, unremarkably denoted by $A$, of a rectangle with the length of $a$ and the width of $b$ is

$$A =\mbox{length}\times\mbox{width}=a\times b$$

In other words, the area of a rectangle is the production of its length and width.
The perimeter is measured in units such equally centimeters, meters, kilometers, inches, feet, yards, and miles. The surface area is measured in units units such as square centimeters $(cm^ii)$, square meters $(yard^2)$, square kilometers $(km^2)$ etc.

The expanse and perimeter of a rectangle work with steps shows the complete step-by-step calculation for finding the perimeter, surface area and diagonal length of the rectangle with the length of $5\;in$ and the width of $10 \;in$ using the perimeter, expanse and diagonal length formulas. For any other values for length and width of rectangle, only supply ii positive existent numbers and click on the GENERATE Work button. The grade school students may employ this area and perimeter of a rectangle to generate the work, verify the results of perimeter and area of ii dimensional figures or do their homework problems efficiently.

Real Earth Problems Using Surface area & Perimeter of a Rectangle

Calculating areas and perimeters of various geometrical figures are very useful in real life problems. Rectangles often appear in existent life. For example, billboards, swimming pools, mobile phones, beds, doors, books. etc. If we need to make a deck along 2 sides of a pond puddle of rectangular shape, we must use the method for finding area of rectangle.
In 3-dimensional geometry, some solids contains rectangular bases. For example, cube, rectangular prism, pyramid, etc. In bug of calculating surface area and volume of these solids we use formula for finding area of rectangle.

Rectangle Practice Problems

Practice Problem 1:
A rectangular garden is $ii$ times long as its wide. If the perimeter of the garden is $48m$, find its surface area.

Practice Trouble 2:
Find the length of the diagonal of a flooring whose dimensions are $36\;in$ by $75\;in$.

The Area Perimeter of a Rectangle calculator, formula, example calculation (work with steps), real earth problems and practice problems would be very useful for grade school students (K-12 pedagogy) to understand the concept of perimeter and area of rectangle. This concept can be of significance in geometry, to find the perimeter and surface area of complex figures, as well as to find surface area and book of some solids. Real life bug on rectangles involving length, width, area, perimeter and diagonal are very common, so this can be of corking the importance of solving.