Formula to calculate the perimeter of a Square

A square is a common geometric shape consisting of 4 sides of equal length and 4 angles, each measuring 90 degrees (referencing Wikipedia's article on squares for a deeper understanding of the nature of this shape) extensively used in solving mathematical and physics problems from elementary to high school. Exercises related to squares are also common with various types of problems such as calculating the perimeter of a square, the area of a square when knowing the side, angles, and combinations of other geometric shapes.

To aid students in memorizing and answering the question of how to calculate the perimeter of a square and apply solving exercises from easy to difficult, Mytour has compiled an article sharing the formula for calculating the perimeter of a square for grade 4, grade 3 in detail with accompanying illustrative example exercises. Let's delve into it!

How to calculate the perimeter of a square in 4th grade and 3rd grade? Formulas and illustrated exercises.

I. What is the formula for calculating the perimeter of a square?

Perimeter is the length of the boundary around a two-dimensional shape, and the perimeter of a square is the length of the boundary around the square. The method of calculating the perimeter is summarized by the following formula:

The formula for finding the perimeter of a square is P = 4a.

Where:

• P represents the perimeter
• a stands for the length of any side

- Statement in words: The perimeter of a square is the sum of the lengths of all its sides; or the perimeter of a square equals 4 times the length of one side of the square.

Using this formula to calculate the perimeter of a square, we can easily derive the formula for the perimeter of a half square as follows:

P/2 = (a x 4)/2
 

II. Application of the formula for calculating the perimeter of a square to solve exercises
 

1. Exercise Type 1: Calculate the perimeter of a square when the length of one side is known

Calculate the perimeter of a square when the length of one side is given. To find the perimeter of square ABCD with dimensions marked on the diagram is a typical exercise for 4th and 3rd-grade students. For this type of exercise, students only need to rely on the given information or use a ruler to accurately measure one side and apply the formula for the perimeter of a square P = 4 x a to solve it.

Solution guide for finding the perimeter of a square when the length of the side is known.

Application Exercise:

Exercise 1: Calculate the perimeter of square ABCD with all sides measuring 4 cm.
Method : 
The perimeter of square ABCD is: 4 x 4 = 16 (cm).
Answer: 16 cm

Calculate the perimeter of a square with side length a, where a = 9 cm. Answer: 36 cm.

Find the perimeter of a square with side length a, given a = 9. Result: 36 cm.

Determine the perimeter of a square knowing the side length is 25 cm. Answer: 100 cm.

Compute the perimeter of a square with dimensions provided in the diagram. To solve, observe the side length of the square in the diagram and apply the formula P = 4 x a for calculation.

Note: Instead of providing the length of the side, the task requests to calculate the area of the square. Alternatively, it may ask for finding the length of the side when given the perimeter of the square. This type of problem can be solved simply by dividing the perimeter of the square by 4 or a = P/4.

2. Exercise Type 2: Calculating the Perimeter of a Square Given the Area

Calculating the perimeter of a square given its area is a problem that requires students to flexibly apply their knowledge of formulas for calculating the perimeter and area of a square. For this type of problem, students need to remember and apply the following concepts:

- Formula for calculating the area of a square: S = a²
- Formula for calculating the perimeter: P = a x 4

Breaking it down:

• S represents the area of a square
• P signifies the perimeter
• a stands for the side length

Formula and guide to calculate the perimeter of a square given the area

* Solution Guide:

To find the perimeter of a square when given the area, follow these steps: Step 1: Use the formula to find the side length of the square (remember to take the square root of the side length). Step 2: Once you have the side length, apply the formula for the perimeter of a square to find the most accurate answer.

* Applied Exercise:

Calculate the perimeter of a square when the area of the square is 16cm²

Solution: Applying the formula for the area of a square: S = a², we get the side length of the square: a² = 16, hence a = 4 (cm). Applying the formula: P = 4a => The perimeter of the square is: 4 x 4 = 16 (cm). Answer: 16 (cm)

Calculating the perimeter of a square inscribed in a circle when the radius is known is an advanced exercise used in middle school math curriculum. To solve this type of problem, you need to remember and understand the following mathematical concepts:

- Concept: A square inscribed in a circle is a square drawn inside a circle in such a way that the 4 corners of the square lie on the circle.

- The distance from the center of the inscribed square to each of its corners = the radius of the circle.

**Solution Guide:**

Step 1: Calculate the length of the square's side:

+ The diagonal of the square divides it into two equal right triangles, each with sides of equal length; the hypotenuse is twice the radius (= 2r).
+ Apply the Pythagorean theorem in the right triangle: a² + b² = c²
Where:

• a, b are the sides of the right angle
• c is the hypotenuse

Reasoning:

The article above has reinforced and expanded upon fundamental knowledge for students, enhancing their understanding of calculating the perimeter of a square in 3rd grade, the perimeter formula for a square in 4th grade, and applying problem-solving in specific cases. Hopefully, the content in this article proves useful, aiding students in becoming familiar with various perimeter calculation exercises and achieving high marks in class. Best wishes for their success.

Squares and equilateral triangles are basic geometric shapes that we encounter in everyday life. If you already know how to calculate the perimeter of a square, consider exploring how to calculate the perimeter of a triangle here.

Mastering the formula for finding the area of quadrilaterals will facilitate easy application to problems involving the area of other special quadrilaterals such as trapezoids, rectangles, squares, etc. You can refer to the formula for finding the area of quadrilaterals on Mytour for further guidance.