Area of a Rectangle: Finding Area based off Perimeter and Vice Versa

Since we know that each pair of opposite sides in a rectangle are equal, we also know that:

$AC=BD=4$

$AB=CD=8$

Now we can calculate the perimeter:

$4\times2=8$

$8\times2=16$

$16+8=24$

Given that in a rectangle all pairs of opposite sides are equal to each other, it can be argued that:

$AB=CD=6$

$AC=BD=4$

Now calculate the perimeter of the rectangle by adding all the sides:

$4+4+6+6=$

$8+12=20$

In other words, the data of the rectangle's area is unnecessary, since we already have all the data to calculate the perimeter, and we do not need to calculate the other sides.

According to the properties of the rectangle, all pairs of opposite sides are equal.

$AB=CD=8$

$AC=BD=2$

Now we calculate the perimeter of the rectangle by adding all the sides:

$4+4+2+2=8+4=12$

We use the formula to calculate the area of a rectangle: length times width:

$AC\times AB=S$

We replace the existing data:

$5\times10=50$

That is, the information that the perimeter of the rectangle is equal to 30 is unnecessary, since all the data to calculate the area already exist and it is not necessary to calculate the other sides.

Given that in a rhombus all opposite sides are parallel and equal to each other, we can state that:

$AC=DB=5$

$AB=CD=9$

Now let's calculate the perimeter by adding all sides together:

$5+9+5+9=10+18=28$

Given that in a rectangle every pair of opposite sides are equal to each other, we can state that:

$\text{AB=CD}=11$

$AC=BD=6$

Now let's calculate the perimeter by adding all the sides together:

$6+11+6+11=12+22=34$

Given that in a rectangle every pair of opposite sides are equal to each other, we can state that:

$AB=CD=7$

$AC=BD=3$

Now let's add all the sides together to calculate the perimeter:

$3+7+3+7=6+14=20$

Given that in a rectangle every pair of opposite sides are equal to each other, we can state that:

$AB=CD=15$

$AC=BD=7$

Now let's calculate all the sides together to find the perimeter of the rectangle:

$7+15+7+15=14+30=44$

Given that in a rectangle every pair of opposite sides are equal to each other, we can state that:

$AB=CD=6$

$AC=BD=3$

To calculate the perimeter of the rectangle, we add all the sides together:

$3+6+3+6=6+12=18$

Given that in a rectangle every pair of opposite sides are equal to each other, we can state that:

$AB=CD=10$

$AC=BD=7$

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

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

Given that in a rectangle every pair of opposite sides are equal to each other, we can state that:

$AB=CD=12$

$AC=BD=8$

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

$8+12+8+12=16+24=40$

Given that in a rectangle every pair of opposite sides are equal to each other, we can state that:

$AB=CD=5$

$AC=BD=2$

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

$2+5+2+5=4+10=14$

Given that in a rectangle every pair of opposite sides are equal to each other, we can state that:

$AB=CD=14$

$AC=BD=8$

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

$8+14+8+14=16+28=44$

Given that in a rectangle every pair of opposite sides are equal to each other, we can state that:

$AB=CD=9$

$AC=BD=7$

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

$7+9+7+9=14+18=32$

Given that in a rectangle every pair of opposite sides are equal to each other, we can state that:

$AB=CD=13$

$AC=BD=6$

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

$6+13+6+13=12+26=38$

The perimeter of the rectangle equals the sum of all its sides, which means:

$P=AB+BC+CD+DA$

Since in a rectangle each pair of opposite sides are equal, we can say that:

$BC=AD=5$

This means that the two sides together equal 10, and now we'll subtract them from the perimeter and get:

$AB+DC=30-10=20$

This means sides AB and DC together equal 20, and since they are equal to each other, we'll divide 20 to find out how much each one equals:

$20:2=10$

Now we'll multiply side AB by side BC to find the area of the rectangle:

$10\times5=50$

The perimeter of the rectangle equals:

$P=AB+BC+CD+DA$

Since we know that BC equals 5 and in a rectangle opposite sides are equal to each other, we get:

$40=AB+5+CD+5$

$40=10+AB+CD$

Since AB equals CD we can write the equation as follows:

$40=2AB+10$

Let's move 10 to the other side and change the sign accordingly:

$40-10=2AB$

$30=2AB$

Let's divide both sides by 2:

$15=AB$

Now we know the length and width of the rectangle and can calculate its area:

$15\times5=75$

After squaring all sides, we can calculate the area as follows:

$4^2=16$

Since we are given that the area of the square equals the area of the rectangle , we will write an equation with an unknown since we are only given one side length of the parallelogram:

$16=1\times x$

$x=16$

In other words, we now know that the length and width of the rectangle are 16 and 1, and we can calculate the perimeter of the rectangle as follows:

$1+16+1+16=32+2=34$