Content

• To step
• Method 1 of 3: Find the perimeter of a square if you know the length of one side
• Method 2 of 3: Find the perimeter of a square if you know its area
• Method 3 of 3: Calculate the perimeter of an inscribed square in a circle if you know the radius

The circumference of a two-dimensional figure is the total distance around the figure, or the sum of the lengths of the sides. The definition of a square is a figure with four equal sides and four right angles (90 °) between those sides. Because all sides have the same length, it is very easy to determine the perimeter of a square! This article will first cover how to calculate the perimeter of a square if you know the length of one of its sides. Then we'll show you how to calculate the circumference if you only know the area, and in the last section we'll teach you how to calculate the circumference of an inscribed square in a circle whose radius length is known.

To step

Method 1 of 3: Find the perimeter of a square if you know the length of one side

1. Think about the formula for the perimeter of a square. For a square where we are the length of the side s the circumference is simply four times the length of that side: Circumference = 4s (note: in the images the letter P is used for the outline, from the English "Perimeter").
2. Find the length of one side and multiply it by 4 to find the circumference. Depending on the assignment, you may need to measure with a ruler or look at other information to determine the length of one side. Here are some examples of perimeter calculations:
   • If the square has a side with a length of 4: Circumference = 4 * 4, in other words 16.
   • If the square has a side with a length of 6: Circumference = 4 * 6, in other words 24.

Method 2 of 3: Find the perimeter of a square if you know its area

1. Know the formula for the area of ​​a square. The area of ​​any rectangle (remember that squares are special rectangles) can be defined as base times height. Since base and height are equal in the case of a square, the area of ​​a square is with side s: s * s. In other words: area = s.
2. Take the square root of the area. The square root of the area gives you the length of one side of the square. For most numbers you need a calculator to calculate the square root. First type in the number, then press the square root (√) key.
   • If the area of ​​the square is 20, then the length of the side is s: =√20 or 4.472
   • If the area of ​​the square is 25, then the length of the side is s = √25 or 5.
3. Multiply the length of the side by 4 to find the circumference. Use the side length value you just found in the formula Circumference = 4s. The result is the perimeter of your square!
   • For a square with an area of ​​20 and a side length of 4.473, the perimeter is: Circumference = 4 * 4.472 or 17,888.
   • For a square with an area of ​​25 and a side length of 5, the perimeter is: Circumference = 4 * 5 or 20.

Method 3 of 3: Calculate the perimeter of an inscribed square in a circle if you know the radius

1. Understand what an inscribed square is. An inscribed square in a circle is a square drawn in a circle with all corners of the square touching the circle.
2. Understand the relationship between the circle's radius and the length of the sides of the square. The distance from the center of an inscribed square to each corner is equal to the radius of the circle. To the side length s To find, we must first imagine cutting the square diagonally in two, so that two equilateral triangles are formed. These triangles have equal sides a and b and a hypotenuse c, which we know is equal to twice the radius of the circle, that is 2r.
3. Use the Pythagorean Theorem to find the side length of the square. The Pythagorean theorem is as follows: in a right triangle, the sum of the squares of the lengths of the sides of the rectangle (a, b) is equal to the square of the length of the hypotenuse (c), a + b = c. Because sides a and b are equal (we're still dealing with a square!) and we know that c = 2r we can now write out the equation and simplify it to find the length of a side:
   • a + a = (2r), now we can simplify:
   • 2a = 4 (r), now divide both sides by 2:
   • (a) = 2 (r), now take the square root of each side:
   • a = √ (2) r. Our length of one side s of the inscribed square = √ (2) r.
4. Multiply the length of one side of the square by four to find the circumference. In this case, the perimeter of the square is: Circumference = 4√ (2) r. The circumference of an inscribed square in a circle is therefore always equal to 4√ (2) r, or approximately 5.657r
5. Solve an example question. We take an inscribed square in a circle with a radius of 10. That means that the diagonal of the square = 2 (10) or 20. The Pythagorean theorem tells us that: 2 (a) = 20, So 2a = 400. Now divide both sides by two and we see that a = 200. Take the square root of each side and we see that a = 14.142. Multiply this by 4 to find the perimeter of your square: Circumference = 56.57.
   • Note: you could have done it this way too: multiply the radius (10) by the number 5.567. 10 * 5.567 = 56.57, but since that might be hard to remember, you better go through the whole process.