Formulas for Rhombus Area and Perimeter, Calculation Techniques

In this guide on calculating perimeter and area, Mytour will provide you with the most precise formulas for calculating area, accompanied by specific examples to facilitate your understanding and practical application.

Calculating Rhombus Area, Perimeter: Methods and Formulas

Exploring the formulae for calculating the area and perimeter of a rhombus.

Defining a Rhombus: A quadrilateral with four sides of equal length.

A rhombus is a special type of parallelogram characterized by its equal side lengths and perpendicular diagonals.

Exploring the Properties of Rhombus:

- A rhombus encompasses all properties of a parallelogram.

Understanding the Formula for Calculating Rhombus Area

- Area Concept of Rhombus: The area of a rhombus is calculated by half the product of its diagonals.

Applying the Diagonal-based Formula

Using the rhombus area formula, with d₁ = 7 cm and d₂ = 9 cm, we obtain the following result:

S = 1/2 x (d₁ x d₂) = 1/2 x (7 x 9) = 1/2 x 63 = 31.5 (cm²).

Example 2: Calculating the area of a rhombus with diagonals measuring 9 cm and 8 cm.
Solution:
Using the formula with rhombus diagonals d₁ = 9cm, d₂ = 8cm, we have:

S = 1/2 x (d₁ x d₂) = 1/2 (9 x 8) = 1/2 x 72 = 36.5 (cm²

* Formula for calculating rhombus area based on base and height

Where:
- h: Height of the rhombus.
- a: Length of the base.

Example: Consider rhombus ABCD with side lengths AB = BC = CD = DA = 4 cm and a height of 3 cm. Calculate the area of the rhombus.

Solution: Using the rhombus area formula, we have h = 3 cm, a = 4 cm. Substituting into the formula, we get the following result:

S = a x h = 3 x 4 = 12 1.5 (cm²).

* Formula for calculating rhombus area based on triangle trigonometric relationships (if the angle of the rhombus is known)

Where: a is the side of the rhombus

Example: Given rhombus ABCD with side length = 4cm and angle A = 35 degrees. Calculate the area of rhombus ABCD.
Solution: Using the formula, we have a = 4, angle = 35 degrees. Substituting into the formula yields:

S = a² x sinA = 4² x sin(35^o) = 9.177 (cm²).

Important Note:
- The unit of area for a rhombus is m², cm², etc.
- When calculating, ensure that the units provided in the question are consistent. If not, convert them to the same unit before proceeding.

3. Formula for calculating the perimeter of a rhombus

- Perimeter concept of a rhombus: The perimeter of a rhombus is calculated by multiplying the length of one side by 4. Here, the number 4 represents the 4 sides of the rhombus.

- Formula for calculating the perimeter of a rhombus: 

Where:
+ P: Perimeter of the rhombus.
+ a: Any side of the rhombus.
- Example: Consider rhombus ABCD with all sides equal to 7 cm. What is the perimeter of this rhombus?

According to the introduced formula for rhombus perimeter, we have a = 7 cm. Thus, the perimeter of rhombus ABCD will be calculated as follows:

P (ABCD) = a x 4 = 7 x 4 = 28 (cm).

4. Formula for calculating the diagonal of a rhombus

Based on the formulas for rhombus perimeter, the formula for calculating rhombus area mentioned above, we can also easily find the formula for calculating the diagonal of a rhombus as follows:

* Calculating the diagonal of a rhombus when the area and the length of one diagonal are known:
If the area of the rhombus and the length of one diagonal (d1) are known, we can easily find the other diagonal of the rhombus using the following formula:  d2 = 2S/ d1.

5. Exercises related to rhombus area and perimeter

With the formula for calculating rhombus perimeter and the formula for calculating rhombus area above, readers surely have acquired useful and important knowledge in dealing with questions, from simple to complex, in exercises or in real life. However, it is also necessary to pay attention to the relationship between the components in the formula for calculating rhombus perimeter and area. Because there will be problems with given answers, requiring you to apply the formulas for calculating rhombus perimeter and area to find the missing variables.

There are even problems linking the formula for calculating rhombus area with the calculation of perimeter and area of a rectangle, area of a circle, applying the formula for calculating the area of a triangle, ... to find other related variables in complex problems. Therefore, you should try to solve as many problems related to the application of formulas for calculating rhombus perimeter and area to improve your problem-solving skills.

A square is a special quadrilateral when it has 4 equal sides and 4 equal angles. In addition, a square also possesses all the properties of a rectangle, understanding how to calculate the area of a rectangle then you can also easily calculate the area of a square, the perimeter of a square. For more information on how to calculate the area of a square, the perimeter of a square, the formulas have been shared on Mytour.

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