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The formula for calculating the area of ​​a parallelogram is knowledge in the 4th grade math curriculum that students need to clearly understand. Therefore, in the following article, Nguyễn Tất Thành will synthesize and analyze fully for you to understand clearly.

What is a parallelogram?

A parallelogram is a type of two-dimensional geometry that has four parallel and equal sides, and two pairs of equal opposite angles. It is also called an equilateral trapezoid.

Parallelogram properties

Parallelograms have several notable properties, including:

• The two diagonals of a parallelogram intersect at their midpoint and divide the parallelogram into two similar triangles.
• Two adjacent sides and two angles at a vertex of a parallelogram are equal.
• The sum of the lengths of the two diagonals of a parallelogram is equal to the sum of the lengths of its four sides.

Formula to calculate the area of ​​a parallelogram

The area of ​​a parallelogram is measured by the size of the surface of the shape, which is the flat surface that people see from the outside.

The formula for calculating the area of ​​a parallelogram is equal to the product of the base multiplied by the height.

S = axh

In there:

• S is the area of ​​the parallelogram.

• a is the base side of the parallelogram.

• h is the height, from the top to the bottom of a parallelogram.

Note: The area of ​​a parallelogram is measured in units of square length, such as square meters (m²), square centimeters (cm²), square millimeters (mm²),…

For example: There is a parallelogram with base length CD = 10 cm and height connecting vertex A to side CD 7 cm long. What is the area of ​​parallelogram ABCD?

Prize:

Based on the formula for calculating the area of ​​a shape, we apply the following problem:

The height of the base side CD (a) is 10cm, the height connecting the bottom to the bottom (h) is 7. At this point, the area of ​​parallelogram ABCD will be

S = axh = 10 x 7 = 70 (cm2).

In addition, there are a number of other formulas to calculate the area of ​​a parallelogram, but they are all based on the basic formula S = ax h. Specifically:

(1) Formula based on the property “Two diagonals of a parallelogram intersect at one point and divide in the ratio 2:1”

S = 1/2 x (d1 + d2) xh

In which: d1 and d2 are the lengths of the two diagonals of the parallelogram

(2) Formula based on the property “The perimeter of a parallelogram is equal to 2 x (a + h)”

S = 1/2 x P xh

Where: P is the perimeter of the parallelogram

(3) The formula is based on the property “Two adjacent sides of a parallelogram form an angle α, and the area of ​​a parallelogram is equal to the product of those two sides multiplied by the sine of angle α”

S = bxcx sin(α)

In there:

• b is the length of one side
• c is the length of the adjacent side corresponding to angle α (angle between two sides)
• sin(α) is the sine of angle α

Some other formulas about parallelograms

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1. Calculate the perimeter of the parallelogram

C = (a + b) x 2

Perimeter = 2 × (Side 1 + Side 2)

2. Calculate the altitude of the parallelogram

h = diagonal/ a

Height = (Diagonal 1 or Diagonal 2) / Side

3. Calculate the diagonal of the parallelogram

Diagonal = √(a^2 + b^2)

Diagonal = √(Side^2 + Side^2)

Formulas for calculating the area of ​​parallelograms in special cases

Below is the formula for calculating the area of ​​a parallelogram in each special case that you should know.

Calculate the area of ​​a parallelogram when only the diagonal is known

When we only know the diagonal of the parallelogram, we can calculate the area of ​​the parallelogram using the following formula:

S = 1/2 x (d1 + d2) xh

In there:

• d1 and d2 are the lengths of the two diagonals of the parallelogram
• h is the height of the parallelogram

However, this formula is only applicable when the two diagonals of the parallelogram are not parallel or perpendicular to each other. If the two diagonals of a parallelogram are parallel or perpendicular to each other, then the area of ​​the parallelogram is unknown.

Calculate the area of ​​a parallelogram when only knowing the lengths of two adjacent sides and the angle between those two sides

When we only know the lengths of two adjacent sides and the angle between those two sides, we can calculate the area of ​​a parallelogram using the following formula:

S = bxcx sin(α)

In there:

• b and c are the lengths of two adjacent sides of the parallelogram
• α is the angle between sides b and c
• sin(α) is the sine of angle α

Other special cases

• If we know that a parallelogram is a square, then the area of ​​the parallelogram is: S = a². Where, a is the side length of the square.
• If we know that a parallelogram is a rectangle, then the area of ​​the parallelogram is: S = ax b. In which: a and b are the lengths of the two sides of the rectangle.

Some popular types of exercises for calculating the area of ​​parallelograms

With knowledge of the area of ​​parallelograms, children will be familiar with the 4th grade math curriculum. During this stage, children will conquer the following types of math exercises:

Form 1: Calculate area when knowing base length and height

Solution method: Correctly apply the standard formula S = axh (S is the area, a is the length of the base, h is the height) to calculate the exact area of ​​the shape.

For example: Let a parallelogram have a base length of 10 cm and a height of 8 cm. Calculate the area of ​​a parallelogram?

Solution: Apply the formula to calculate the area of ​​a parallelogram: S = 10 x 8 = 80 cm². So, the area of ​​the parallelogram is 80 cm².

Form 2: Calculate the base length when knowing the area and height of the parallelogram

Solution method: From the standard formula S=axh, we deduce the formula to calculate the base length as follows: a = S : h

For example: Let a parallelogram have an area of ​​54 cm² and a height of 6 cm. Calculate the length of the base of a parallelogram?

Solution: Apply the formula to calculate the base length of a parallelogram: a = 54 / 6 = 9 cm. So, the length of the base of the parallelogram is 9 cm.

Form 3: Calculate the height when knowing the area and base length of the parallelogram

Solution method: From the formula S=axh, we deduce the formula to calculate the height of the shape as h = S : a

For example: Let’s say a parallelogram has a base length of 12 cm and an area of ​​72 cm². Calculate the height of a parallelogram?

Solution: Apply the formula to calculate the height of a parallelogram: h = 72 / 12 = 6 cm. So, the height of the parallelogram is 6 cm.

Form 4: General exercises

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Solution method: You need to read the problem carefully, determine the math format in the problem and come up with the correct solution. It will usually be a form of math with text explanations and application of theory as multiple-choice questions.

Exercises about the area of ​​parallelograms for children to practice on their own

Below are some exercises on calculating the area of ​​parallelograms for you to practice:

Exercise 1: Let the parallelogram ABCD have a base length of 8 cm and a height of 6 cm. Calculate the area of ​​parallelogram ABCD.

Exercise 2: Let the parallelogram ABCD have an area of ​​24 cm² and a height of 3 cm. Calculate the length of the base of parallelogram ABCD.

Exercise 3: Let the parallelogram ABCD have a base length of 12 cm and an area twice the height. Calculate the height of parallelogram ABCD.

Exercise 4: Let the parallelogram ABCD have two diagonals AC and BD perpendicular at O. Let I be the intersection of the two diagonals. Know AC = 12 cm, BD = 15 cm and IO = 6 cm. Calculate the area of ​​parallelogram ABCD.

Exercise 5: A parallelogram-shaped piece of land has an area of ​​120 m² and a height of 10 m. Calculate the length of the base of the parallelogram.

Exercise 6: A parallelogram-shaped table has an area of ​​160 cm² and a height of 8 cm. Calculate the length of the base of the parallelogram table.

Exercise 7: A parallelogram fabric has a base length of 15 m and an area twice the height. Calculate the height of the parallelogram cloth.

Exercise 8: A parallelogram football field has an area of ​​200 m² and two diagonals are perpendicular at O. Let I be the intersection of the two diagonals. Know that diagonal AC = 20 m and IO = 5 m. Calculate the area of ​​the parallelogram football field.

Exercise 9: A parallelogram-shaped piece of land has an area 3 times the area of ​​a rectangular piece of land with a length of 10 m and a width of 8 m. Calculate the length of the base of the parallelogram.

Exercise 10: A parallelogram cloth has an area twice the area of ​​a rectangular cloth with a length of 12 m and a width of 7 m. Calculate the height of the parallelogram fabric.

Tips to help children do exercises to calculate the area of ​​parallelograms effectively

To help children remember and know how to do homework about this knowledge, parents can immediately apply the following tips:

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Firmly grasp the theory and formula for calculating the area of ​​a parallelogram

To solve exercises about parallelograms, students are required to have a solid grasp of the theory. Especially with area calculation exercises, children must clearly understand the standard formula S = axh, so that they can easily apply the formula to solve the exercise most accurately.

Regular practice is important

After understanding the theory, parents should practice more with their children Do exercises together in textbooks, assigned exercises, learn more reference materials on the internet, practice exam questions,… This will help stimulate children’s brain and thinking ability when learning math better.

Learn the formula for calculating the area of ​​a parallelogram through poetry

To help children easily remember geometric formulas, many teachers have come up with poems and puzzles. With the formula for calculating the area of ​​a parallelogram, we have a verse that is quite easy to learn and remember such as:

“Area of ​​a parallelogram

Length times base – calculate quickly!”

Or:

“Calculate the area of ​​a parallelogram

The height multiplied by the bottom is not difficult

What is needed for circumference?

Next to each other, when we add up, we multiply by two.”

Some notes when calculating the area of ​​a parallelogram

In the process of solving parallelogram area exercises, you need to pay attention to the following issues:

• Read and analyze the question carefully to clearly understand the requirements and give accurate answers, avoiding confusion.

• Note that the units when calculating area must be the same. If it is cm2, it must be cm2. If it is different, it must be converted to the same unit of measurement.

• You should carefully observe the picture and combine the theory to solve the exercises correctly.

Conclude

Above is the basic knowledge about the area of ​​parallelograms. Hopefully, based on these shares, we will help you solve exercises and apply them in practice in the most accurate way.

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