Calculate the perimeter of a rectangle is something very simple that sometimes it is useful to remember how to do it. First of all, let's refresh the concept of perimeter, a word that tells us the sum of the length of all the sides of a geometric figure.
Formula for calculating the perimeter of a rectangle
We already know that the rectangle has two even sidesthat is, there are two sides of type 'a' and two sides of type 'b', so that the perimeter of a rectangle is calculated by the following mathematical formula:
- Perimeter of the rectangle = a + b + a + b = 2a + 2b
Like practical example From the above, let's imagine a rectangle whose side a=3 cm and side b=7 cm. From the above formula we know that:
- Perimeter = (2 x 3 cm) + (2 x 7 cm) = 6 cm + 14 cm = 20 centimeters.
Perimeter of a rectangle with diagonal
Some exercises may ask us to calculate the perimeter of a rectangle starting from its diagonal. To solve the problem, it is essential that we are given one more piece of information: the length of one of the sides. If we are given the diagonal and the length of one side of the figure, we can calculate its perimeter easily with the Theorem of Pythagoras.
As a solved exercise we are going to take out the perimeter of a rectangle whose diagonal measures 16 cm and its short side measures 4 centimeters.
As you know, a rectangle has two exactly equal diagonals so we have taken the right triangle that forms one of them to apply Pythagoras. In the problem statement we are given that c = 16cm and side a = 4cm. With these data we can find out how long side b is, that is, the one we are missing to be able to calculate the perimeter.
To do this, go to the Pythagoras formula and clear b to get its value:
b = √(c2 - a2)
Now that we know how to calculate the missing unknown, we substitute into the equation and solve:
b = √(162 – 42) = √(256 - 16) = √240 = 15,49 cm
We can now calculate the perimeter of the rectangle with the formula that we have seen in the previous point because we already know how long all its sides are:
perimeter = 2 x 4cm + 2 x 15,49 cm = 38,98 cm
In the in case they only give us the diagonal and we are asked to calculate the perimeter, we have 2 options:
- Invent the length of one of the sides and solve. With the obtained result we justify that we have calculated the perimeter of a rectangle whose diagonal is the one indicated in the statement.
- Let the result be expressed as a function of the sides a and b of the rectangle using algebraic expressions.
If you have any doubts about how to do it, leave us a comment and we will help you as soon as possible.
Calculate the perimeter from the area of the rectangle.
If you want to calculate the perimeter of the rectangle from its areathen we have to know the following formula:
- Area of rectangle = a * b
As you can see, we also we have two unknowns so it is essential that the problem statement gives us the area and the length of one of the sides. With that, we clear in the equation, solve and apply the formula to obtain the perimeter.
If we are not given the length of any sideIf we are asked to calculate the perimeter of a rectangle, we can invent how long one of them is because we will create a system that satisfies the result. For example, if we are asked to calculate the perimeter from a rectangle whose area measures 24 cm2We can assume that one of the sides measures 6 cm, so the other will measure 6 cm:
side a = area / side b = 24 / 6 = 4 cm
Now we can obtain how long the contour of the figure is:
contour = 4 + 4 + 4 + 6 + 6 + 6 = 20 cm
Does this rectangle satisfy the condition that its area is equal to 24 cm?2? Yes, therefore, we have provided one of the many solutions that exist for this exercise.
If you prefer, you can save yourself the above calculation with our calculator to obtain the area of a rectangle.