Perimeter of a Parallelogram - Examples, Exercises and Solutions

First we need to remember that pairs of opposite sides in a parallelogram are parallel and equal.

Therefore, AB is parallel to CD and BC is parallel to AD.

From this we can conclude that AB = CD = 7.

Also: BC = AD = 12.

Finally we can calculate the perimeter by adding all the sides together:

$7+7+12+12=14+24=38$

As is true for a parallelogram each pair of opposite sides are equal and parallel,

Therefore it is possible to argue that:

$AC=BD=7$

$AB=CD=10$

Now we can calculate the perimeter of the parallelogram by adding together all of its sides:

$10+10+7+7=20+14=34$

As is true for a parallelogram every pair of opposite sides are equal:

$AB=CD=6,AC=BD=4$

The perimeter of the parallelogram is equal to the sum of all sides together:

$4+4+6+6=8+12=20$

Each pair of opposite sides are parallel and equal.

AB is parallel to DC and therefore also AB = DC = 8.

We will use the given perimeter to find AD and BC—which are also equal and parallel to each other.

Let's now calculate the perimeter of the parallelogram:

$24=2AB+2AD$

$24=16+2AD$

$24-16=2AD$

$8=2AD$

Then, we'll divide the two sides by 2:

$\frac{8}{2}=\frac{2AD}{2}$

$AD=4$

The area of a parallelogram is equal to the side multiplied by the height of that side.

First, find the value of AB using the parallelogram area formula:

$AB\times h=S$

$AB\times3=39$

$\frac{3AB}{3}=\frac{39}{3}$

$AB=13$

Since in a parallelogram all pairs of opposite sides are equal and parallel, we can find the perimeter of the parallelogram:

$2AB+2AC=2\times13+2\times8=26+16=42$

Since in a parallelogram each pair of opposite sides are equal and parallel:

$BC=AD=2x$

$AB=CD=x$

Now let's substitute the known data into the formula for calculating the perimeter:

$80=2x\times2+2\times x$

$80=4x+2x$

$80=6x$

Let's divide both terms by 6:

$\frac{80}{6}=\frac{6x}{6}$

$\frac{80}{6}=x$

Let's simplify the fraction by 2

$\frac{40}{3}=x$

As is true of a parallelogram each pair of opposite sides are equal to one another

$AB=CD,AC=BD$

Given that AB > AC

Let's call AC by the name X and therefore:

$AB=2AC=2\times x=2x$

Now we know that:

$AB=CD=2x,AC=BD=x$

The perimeter is equal to the sum of all the sides together:

$2x+x+2x+x=6x$

As is true for a parallelogram each pair of opposite sides are equal:

$AB=CD=6,AC=BD=x$

Calculate X according to the given perimeter:

$20=6+6+x+x$

$20=12+2x$

$20-12=2x$

$8=2x$

$x=4$

In a parallelogram, each pair of opposite sides are equal and parallel: AB = CD and AC = BD.

Given that the length of one side is 4 times greater than the other side equal to X, we know that:

$AB=CD=4AC=4BD$

Now we replace the data in this equation with out own (assuming that AB = CD = X):

$x=x=4AC=4BD$

We divide by 4:

$\frac{x}{4}=\frac{x}{4}=AC=BD$

Now we calculate the perimeter of the parallelogram and express both AC and BD using X:

$P=x+\frac{x}{4}+x+\frac{x}{4}$

$P=2x+\frac{x}{4}+\frac{x}{4}=2\frac{1}{2}x$

As is true for a parallelogram each pair of opposite sides are equal to one other:

$AB=CD=4x,AC=BD=2x$

To begin we will find X through the perimeter:$60=2x+4x+2x+4x$

$60=12x$

$x=5$

Next we will calculate all of the sides of the parallelogram:

$AB=CD=4\times5=20$

$AC=BD=2\times5=10$

Hence the area of the parallelogram will be equal to:

$CD\times3=20\times3=60$

The perimeter of the parallelogram is calculated as follows:

$S_{ABCD}=AB+BC+CD+DA$ Since ABCD is a parallelogram, each pair of opposite sides is equal, and therefore, AB=DC and AD=BC

According to the figure that the side of the parallelogram is 2 times larger than the side adjacent to it, it can be argued that$AB=DC=2BC$

We inut the data we know in the formula to calculate the perimeter:

$P_{ABCD}=2BC+BC+2BC+BC$

We replace the given perimeter in the formula and add up all the BC coefficients accordingly:

$24=6BC$

We divide the two sections by 6

$24:6=6BC:6$

$BC=4$

We know that$AB=DC=2BC$We replace the data we obtained (BC=4)

$AB=DC=2\times4=8$

As ABCD is a parallelogram, then all pairs of opposite sides are equal, therefore BC=AD=4

To find EC we use the formula:$A_{ABCD}=AB\times EC$

We replace the existing data:

$24=8\times EC$

We divide the two sections by 8$24:8=8EC:8$

$3=EC$

Let's call CE as X

According to the data

$AB=x+2,AD=x-3$

The perimeter of the parallelogram:

$2(AB+AD)$

$38=2(x+2+x-3)$

$38=2(2x-1)$

$38=4x-2$

$38+2=4x$

$40=4x$

$x=10$

Now it can be argued:

$AD=10-3=7,CE=10$

The area of the parallelogram:

$CE\times AD=10\times7=70$