Examples with solutions for Area of a Parallelogram: Finding Area based off Perimeter and Vice Versa

Exercise #1

ABCD is a parallelogram.

Its perimeter is 47 cm.

What is its area?

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Video Solution

Step-by-Step Solution

First, let's remember that the perimeter of a parallelogram is the sum of its sides,

which is

AB+BC+CD+DA

We recall that in a parallelogram, opposite sides are equal, so
BC=AD=6

Let's substitute in the formula:

2AB+12=47

2AB=35

AB=17.5

Now, after finding the missing sides, we can continue to calculate the area.

Remember, the area of a parallelogram is side*height to the side.

17.5*8= 140

Answer

140 140 cm²

Exercise #2

ABCD is a parallelogram with a perimeter of 38 cm.

AB is twice as long as CE.

AD is three times shorter than CE.

CE is the height of the parallelogram.

Calculate the area of the parallelogram.

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Video Solution

Step-by-Step Solution

Let's call CE as X

According to the data

AB=x+2,AD=x3 AB=x+2,AD=x-3

The perimeter of the parallelogram:

2(AB+AD) 2(AB+AD)

38=2(x+2+x3) 38=2(x+2+x-3)

38=2(2x1) 38=2(2x-1)

38=4x2 38=4x-2

38+2=4x 38+2=4x

40=4x 40=4x

x=10 x=10

Now it can be argued:

AD=103=7,CE=10 AD=10-3=7,CE=10

The area of the parallelogram:

CE×AD=10×7=70 CE\times AD=10\times7=70

Answer

70 cm²

Exercise #3

ABCD is a parallelogram whose perimeter is equal to 24 cm.

The side of the parallelogram is two times greater than the adjacent side (AB>AD).

CE is the height of the side AB

The area of the parallelogram is 24 cm².

Find the height of CE

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Video Solution

Step-by-Step Solution

The perimeter of the parallelogram is calculated as follows:

SABCD=AB+BC+CD+DA 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 thatAB=DC=2BC AB=DC=2BC

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

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

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

24=6BC 24=6BC

We divide the two sections by 6

24:6=6BC:6 24:6=6BC:6

BC=4 BC=4

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

AB=DC=2×4=8 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:AABCD=AB×EC A_{ABCD}=AB\times EC

We replace the existing data:

24=8×EC 24=8\times EC

We divide the two sections by 824:8=8EC:8 24:8=8EC:8

3=EC 3=EC

Answer

3 cm

Exercise #4

The parallelogram ABCD contains the rectangle AEFC inside it, which has a perimeter of 24.

AE = 8

BC = 5

P=24P=24P=24555AAABBBCCCDDDEEEFFF8

What is the area of the parallelogram?

Video Solution

Step-by-Step Solution

In the first step, we must find the length of EC, which we will identify with an X.

We know that the perimeter of a rectangle is the sum of all its sides (AE+EC+CF+FA),

Since in a rectangle the opposite sides are equal, the formula can also be written like this: 2AE=2EC.

We replace the known data:

2×8+2X=24 2\times8+2X=24

16+2X=24 16+2X=24

We isolate X:

2X=8 2X=8

and divide by 2:

X=4 X=4

Now we can use the Pythagorean theorem to find EB.

(Pythagoras: A2+B2=C2 A^2+B^2=C^2 )

EB2+42=52 EB^2+4^2=5^2

EB2+16=25 EB^2+16=25

We isolate the variable

EB2=9 EB^2=9

We take the square root of the equation.

EB=3 EB=3

The area of a parallelogram is the height multiplied by the side to which the height descends, that isAB×EC AB\times EC .

AB= AE+EB AB=\text{ AE}+EB

AB=8+3=11 AB=8+3=11

And therefore we will apply the area formula:

11×4=44 11\times4=44

Answer

44

Exercise #5

Look at the parallelogram of the figure.

The perimeter of the parallelogram is 44 cm.

Calculate the area.

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Video Solution

Answer

84 84 cm².

Exercise #6

Given the parallelogram of the figure

Its perimeter is 30 cm

What is your area?

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Video Solution

Answer

66 66 cm².

Exercise #7

Look at the parallelogram in the figure below.

Its perimeter is 50 cm.

What is its area?

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Video Solution

Answer

It is not possible to calculate.

Exercise #8

Look at the parallelogram in the figure.

Its perimeter is 70 cm.

What is its area?

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Video Solution

Answer

54 54 cm².

Exercise #9

Given the parallelogram of the figure

The area is equal to 63 cm².

Find the perimeter

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Video Solution

Answer

36 36 cm

Exercise #10

If area of the parallelogram in the figure is 48 cm², then what is the perimeter?

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Video Solution

Answer

32 32 cm

Exercise #11

The area of the parallelogram in the figure is 145 cm².

What is its perimeter?

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Video Solution

Answer

70 70 cm

Exercise #12

Look at the parallelogram in the figure below.

If its area is 75 cm², then what is its perimeter?

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Video Solution

Answer

It is not possible to calculate.

Exercise #13

The area of parallelogram ABCD is 208 cm².

What is its perimeter?

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Video Solution

Answer

66 66 cm

Exercise #14

ABCD is a parallelogram whose perimeter is equal to 22 cm.

AC=4 height of the parallelogram for side CD is 3 cm

Calculate the area of the parallelogram

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Video Solution

Answer

21 cm².

Exercise #15

ABCD is a parallelogram whose perimeter is equal to 22 cm.

Side AB is smaller by 5 than side AD

The height of the parallelogram for the side AD is 2 cm

What is the area of the parallelogram?

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Video Solution

Answer

16 cm²