Formula for calculating the perimeter of a Diamond

A diamond is a quadrilateral with four equal sides, also known as a Rhombus. How do you calculate the perimeter of a diamond? This is a common question for students when learning this topic. If you still have questions, refer to our article below to enhance your knowledge about diamonds and how to calculate the perimeter of a diamond.

Formula for calculating the perimeter of a Diamond with illustrative examples
 

A diamond is a quadrilateral with 4 equal sides or a parallelogram with two equal sides/2 diagonals perpendicular to each other. For more information, check Wikipedia's article on Diamonds. 
 

1. Formula for calculating the perimeter of a Diamond

Similar to calculating the perimeter of a square, the perimeter of a diamond can be calculated as follows:

Perimeter (P) = side length x 4

Where:
- P is the perimeter of the diamond
- a is the length of the side

The formula can be expressed as follows: The perimeter of a diamond is equal to the length of one side multiplied by 4 or 4 times the length of one side.

2. Exercises on calculating the perimeter of a diamond 

2.1. Calculate the perimeter of a diamond given the side length

Solution: Apply the formula: P = side length x 4

Exercise 1: Calculate the perimeter of a diamond given the side length = 10 dm.

Solution: Applying the formula for calculating the perimeter of a diamond, we have:

The perimeter of the diamond is: 10 x 4 = 40 (dm)

Exercise 2: Following the instructions above, solve the exercise to find the perimeter of a diamond, knowing the side lengths are respectively:

a) 9 cm b) 20 dm c) 3/4 m d) 5.6 cm

Solution:

a) The perimeter of the diamond is: 9 x 4 = 36 (cm)
b) The perimeter of the diamond is: 20 x 4 = 80 (dm)
c) The perimeter of the diamond is: 3/4 x 4 = 4 (m)
d) The perimeter of the diamond is: 5.6 x 4 = 22.4 (cm)
 

2.2. Calculate the perimeter of a diamond given the area and the length of two diagonals

Solution: Apply the formulas for calculating the perimeter and area of a diamond: P = side length x 4 and S = 1/2 x d1 x d2

Exercise 3: Calculate the perimeter of a diamond given the diagonals measuring 16 cm and 30 cm

Let the side of the diamond be denoted by a, and the diagonals be d1 and d2 respectively

- Applying the Pythagorean theorem in the right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs. We have: a² = (d1/2)² + (d2/2)²= (8)² + (15)²  or a = 17

The perimeter of the diamond: P = 4 x a = 68.
 

3. Notes on Diamonds

- A diamond has two diagonals perpendicular to each other, and the main diagonal is the bisector of the diamond's angles.
- The two diagonals of a diamond are its axes of symmetry, and the intersection of the two main diagonals is the center of symmetry.
- If a diamond has a right angle, it is also a square (the remaining three angles will also be right angles).

=> These pieces of knowledge are quite useful for students, making it easier for them to solve problems related to calculating the perimeter of a diamond.

4. How to draw a standard Diamond ABCD quickly and simply

Method 1 : Draw a diamond using a ruler and compass

Step 1: Draw any line AC and determine the midpoint O of that line.
Step 2:: Use a compass to draw line BD perpendicular to AC at O, with O as the midpoint of BD.
Step 3:: Connect vertices A to B, B to C, C to D, D to A => forming the diamond ABCD.

Method 2 : Draw a diamond using a ruler and compass

Step 1: Draw line AC of any length.
Step 2:: Use a compass, open it wider than 1/2 AC. Draw a circle centered at A and another at C so that the two circles intersect at two points, named B and D.
Step 3:: Connect points A, B, C, D => forming the diamond ABCD.

In this article, we not only provide you and students with the formula for calculating the perimeter of a diamond, solve various exercises related to the perimeter of a diamond, but also guide students on how to draw a diamond simply and quickly. We hope this is valuable knowledge for students studying diamonds. Additionally, parents can also refer to our article on calculating the area of a diamond to help their children study effectively at home.

Students can also refer to the article on calculating the diagonal of a diamond given the side length and angle, which is a common type of exercise that students may encounter in problems related to diamonds.