Exercises on the area of parallelograms

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You parallelogramsthey are polygons four-sided, which have opposite sides parallel, two by two. Examples of parallelograms are: o square, O rectangle it's the diamond.

The area (A) of any parallelogram corresponds to the measure of its surface and can be determined by the following formula:

$\dpi{120} \mathbf{A = b \cdot h}$

On what:

B: measure of the base of the parallelogram;
H: height of the parallelogram.

To learn more about this subject, check out a list of exercises on the parallelogram area, with all resolutions of the issues.

Index

Exercises on the area of parallelograms
Resolution of question 1
Resolution of question 2
Resolution of question 3
Resolution of question 4

Exercises on the area of parallelograms

Question 1. Determine the area of the parallelogram with the dimensions shown in the figure below:

Question 2. Determine the area of the parallelogram with the dimensions shown in the figure below:

Question 3. Determine the colored surface area of the figure below:

Question 4. Determine the area of the parallelogram with dimensions shown in the figure below:

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Resolution of question 1

We have b = 10 cm and h = 8 cm. Let's substitute these values into the parallelogram area formula:

$\dpi{120} \mathrm{A = b \cdot h}$

$\dpi{120} \Rightarrow \mathrm{A = 10 \cdot 8}$

$\dpi{120} \Rightarrow \mathrm{A = 80}$

Therefore, the parallelogram area is equal to 80 cm².

Resolution of question 2

We have b = 8 cm and h = 12 cm. Let's substitute these values into the parallelogram area formula:

$\dpi{120} \mathrm{A = b \cdot h}$

$\dpi{120} \Rightarrow \mathrm{A = 8 \cdot 12}$

$\dpi{120} \Rightarrow \mathrm{A = 96}$

Therefore, the parallelogram area is equal to 96 cm².

Resolution of question 3

The colored surface area corresponds to the area of the major parallelogram minus the area of the major parallelogram.

Let's calculate the area of each parallelogram separately.

Larger parallelogram:

We have b = 7 cm + 2 cm = 9 cm and h = 10 cm + 1 cm = 11 cm. Let's substitute these values into the parallelogram area formula:

$\dpi{120} \mathrm{A = b \cdot h}$

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$\dpi{120} \Rightarrow \mathrm{A = 9 \cdot 11}$

$\dpi{120} \Rightarrow \mathrm{A = 99}$

Minor parallelogram:

We have b = 7 cm and h = 10 cm. Let's substitute these values into the parallelogram area formula:

$\dpi{120} \mathrm{A = b \cdot h}$

$\dpi{120} \Rightarrow \mathrm{A = 7 \cdot 10}$

$\dpi{120} \Rightarrow \mathrm{A = 70}$

So, the colored surface area is given by:

$\dpi{120} \mathrm{A_{colored} = A_{larger} - A_{smaller}}$

$\dpi{120} \Rightarrow \mathrm{A_{colored} = 99 -70}$

$\dpi{120} \Rightarrow \mathrm{A_{colored} = 29}$

Therefore, the colored surface area is equal to 29 cm².

Resolution of question 4

To calculate the area of the parallelogram, we need to determine the measure of its base, that is, the measure of the side. $\dpi{120} \overline{BC}$ .