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

The area of a rectangle is equal to 8.

Calculate the perimeter of the rectangle.

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:

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

12

The area of the rectangle shown below is equal to 10.

Calculate the perimeter of the rectangle.

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

$AB=CD=5$

$AC=BD=2$

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

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

14

The area of the rectangle below is equal to 18.

Calculate the perimeter of the rectangle.

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

$AB=CD=6$

$AC=BD=3$

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

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

18

The area of a rectangle is equal to 32.

Calculate the perimeter of the rectangle.

Since we know that in a rectangle, each pair of opposite sides are equal to each other, we can claim that:

$AC=BD=4$

$AB=CD=8$

Now we can calculate the perimeter:

$4\times2=8$

$8\times2=16$

$16+8=24$

24

The area of a rectangle is 21.

Work out the perimeter of the rectangle.

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

$AB=CD=7$

$AC=BD=3$

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

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

20

The area of the rectangle below is equal to 24.

Calculate the perimeter of the rectangle.

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.

20

The area of the rectangle below is equal to 45.

Calculate the perimeter of the rectangle.

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

$AC=DB=5$

$AB=CD=9$

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

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

28

The area of the rectangle below is equal to 66.

Calculate the perimeter of the rectangle.

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

$\text{AB=CD}=11$

$AC=BD=6$

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

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

34

The area of a rectangle is equal to 70.

Calculate the perimeter of the rectangle.

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

$AB=CD=10$

$AC=BD=7$

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

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

34

The area of the rectangle below is 63.

Calculate the perimeter of the rectangle.

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

$AB=CD=9$

$AC=BD=7$

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

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

32

The area of the rectangle below is equal to 96.

Calculate the perimeter of the rectangle.

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

$AB=CD=12$

$AC=BD=8$

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

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

40

The area of a rectangle is 78.

Calculate the perimeter of the rectangle.

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

$AB=CD=13$

$AC=BD=6$

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

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

38

The area of a rectangle is equal to 105.

Calculate its perimeter using the data in the figure below.

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

$AB=CD=15$

$AC=BD=7$

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

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

44

The perimeter of the rectangle below is equal to 30.

What is the area of the rectangle?

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.

50

The area of the rectangle is 112.

Calculate the perimeter of the rectangle.

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

$AB=CD=14$

$AC=BD=8$

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

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

44

The area of the square whose side length is 4 cm is
equal to the area of the rectangle whose length of one of its sides is 1 cm.

What is the perimeter of the rectangle?

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:

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

34

Look at the rectangle in the figure.

Its perimeter is 30 cm.

What is its area?

50 cm²

ABCD is a rectangle.

BC = 5

Perimeter = 40

Calculate the area of the rectangle.

75