3 Ways to Calculate the Perimeter of a Square

2024 Author: Samantha Chapman | [email protected]. Last modified: 2024-02-02 02:12

The perimeter of a square, like that of any geometric shape, is the measure of the length of the outline. The square is a regular quadrilateral, which means it has four equal sides and four right angles. Since all sides are the same, it is not difficult to calculate the perimeter! This tutorial will first show you how to calculate the perimeter of a square whose side you know and then that of a square whose area you know. Finally it will treat a square inscribed in a circumference of known radius.

Steps

Method 1 of 3: Calculate the Perimeter of a Square with a Known Side

Step 1. Remember the formula for calculating the perimeter of a square

For a square on the side s, the perimeter is simply: P = 4s.

Step 2. Determine the length of one side and multiply it by four

Depending on the task assigned to you, you will need to take the value of the side with a ruler or deduce it from other information. Here are some examples:

• If the side of the square measures 4, then: P = 4 * 4 = 16.
• If the side of the square measures 6, then: P = 6 * 6 = 64.

Method 2 of 3: Calculate the Perimeter of a Square of Known Area

Step 1. Review the formula for the area of the square

The area of each rectangle (remember that the square is a special rectangle) is defined as the product of the base by the height. Since both the base and the height of a square have the same value, one square on each side s owns the area equal to s * s that is: A = s².

Step 2. Calculate the square root of the area

This operation gives you the side value. In most cases you will have to use a calculator to extract the root: type the area value and then press the square root key (√). You can also learn how to calculate the square root by hand!

• If the area is equal to 20, then the side is equal to s = √20 that is 4, 472.

• If the area is equal to 25, then the side is equal to s = √25 that is

  Step 5..

Step 3. Multiply the side value by 4 and you will get the perimeter

Take the length s you just got and put it in the perimeter formula: P = 4s!

• For the square of area equal to 20 and side 4, 472, the perimeter is P = 4 * 4, 472 that is 17, 888.

• For the square of area equal to 25 and side 5, the perimeter is P = 4 * 5 that is

  Step 20..

Method 3 of 3: Calculate the Perimeter of a Square Inscribed in a Circle of Known Radius

Step 1. Understand what an inscribed square is

The geometric shapes inscribed in others are very often present in tests and in class assignments, so it is important to know them and know how to calculate the various elements. A square inscribed in a circle is drawn inside the circumference so that the 4 vertices lie on the circumference itself.

Step 2. Review the relationship between the radius of the circle and the length of the side of the square

The distance from the center of the square to one of its corners is equal to the value of the radius of the circumference. To calculate the length s of the side, you must first imagine that you cut the square diagonally and form two right triangles. Each of these triangles has legs to And b equal to each other and a hypotenuse c you know because it is equal to the diameter of the circumference (twice the radius or 2r).

Step 3. Use the Pythagorean Theorem to find the length of the side

This theorem states that for any right triangle with legs to And b and the hypotenuse c, to² + b² = c². So long as to And b are equal to each other (remember that they are also the sides of a square!) then you can say that c = 2r and rewrite the equation in simplified form as follows:

• to² + a² = (2r)² ', now simplify the equation:
• 2a² = 4 (r)², divide both sides of equality by 2:
• (to²) = 2 (r)², now extract the square root from both values:
• a = √ (2r). The length s of a square inscribed in a circle is equal to √ (2r).

Step 4. Multiply the side length value by 4 and find the perimeter

In this case the equation is P = 4√ (2r). For the distributive property of the exponents you can say that 4√ (2r) It's equal to 4√2 * 4√r, so you can further simplify the equation: the perimeter of each square inscribed in a circle with a radius r is defined as P = 5.657r

Step 5. Solve the equation

Consider a square inscribed in a circle of radius 10. This means that the diagonal is equal to 2 * 10 = 20. Use the Pythagorean Theorem and you will know that: 2 (a²) = 20², so 2a² = 400.

Now divide both sides in half: to² = 200.

Extract the root and find that: a = 14, 142. Multiply this result by 4 and find the perimeter of the square: P = 56.57.

Note that you could have achieved the same result by simply multiplying the radius (10) by 5,657. So: 10 * 5, 567 = 56, 57; however it is not easy to remember this constant during an exam, it is much better to learn the procedure explained here.