how to find the perimeter of a circle

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The perimeter is the length of an outline of a shape. The general way to find the perimeter of any shape is to add up the length of all its sides. For certain shapes, such as rectangles and circles, there are specific formulas you can use to simplify the process. In other instances, you might be missing one or more of the side lengths, but are given other information. In cases like this, you must complete extra steps to find the missing side length before you can calculate the perimeter.

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   Perimeter is defined as the length surrounding a given area. Imagine you had a fence that runs around your entire property. In order to find the total length of the fence, you'd need to calculate the perimeter. Measuring the entire fence by hand is one way to do it, but an easier way is to use the perimeter formula.^[1]

   • You might not be given the length of all 4 sides, which is another reason why you'd need to use an equation to find the perimeter instead of just addition.

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   Circumference is the perimeter of a circle. Since a circle doesn't have any straight lines, the method for figuring out its perimeter is a little bit different. It involves using Pi and the radius or diameter of the entire shape.^[2]

   • You can't find the perimeter of a circle just by measuring it; you have to use the circumference equation.

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   Express the perimeter in distance units. These are feet, inches, centimeters, miles, etc. Since you're measuring the length of something, you always have to use real-world distance units when you get your answer.^[3]

   • You'll have to make sure all your units are the same before you do your equation, too. This might mean changing feet to inches, miles to feet, or anything in between.

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   Use an online calculator to check your answer. Although you might have to show your work on your homework or assignment, you can always use an online calculator to double check that you're doing it right. Search for the shape you're working on + perimeter in a web browser to find free online calculators that you can use.^[4]

   • Make sure you're using a calculator for your specific shape.

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   Set up the formula for the perimeter of a rectangle. The formula is ${\displaystyle P=2(w+h)}$ , where ${\displaystyle P}$ equals the perimeter of the rectangle, ${\displaystyle w}$ equals the width of the rectangle, and ${\displaystyle h}$ equals the height of the triangle. If you don't know the length of the width and height of the rectangle, you cannot use this formula.^[5]

   • You can also use the formula ${\displaystyle P=a+b+c+d}$ , where each variable is equal to the length of one side of the rectangle. A variable is any number in your equation that you use, signified by letters (a, b, c, d).
   • If you don't know the height and width of your shape, you can plug in the information you do know, like the area, the length of one side, or the length of the diagonal.

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   Plug the width and height into the formula. It doesn't matter which measurement you use for the width and which you use for the height since the width and height are two adjacent sides. If the rectangle is not a square, these side lengths must be different.^[6]

   • For example, if a rectangle has a width of 5 cm and a height of 10 cm, your formula will look like this: ${\displaystyle P=2(5+10)}$ .

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   Add the length and width, and multiply by 2. Make sure you follow the order of operations and complete the calculation in parentheses before multiplying. The resulting value will give you the perimeter of your rectangle.^[7]

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   Find the perimeter given other information. Often you will not be given the length of all sides, or even the length of any side. It still may be possible to find the perimeter of a rectangle.^[9]

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   Set up the formula for finding the perimeter of a triangle. The formula is ${\displaystyle P=a+b+c}$ , where the variables equal the three sides of the triangle. This formula is the same whether or not the triangle is right. You must have all side lengths to use this formula. If you know that you have an equilateral triangle, you only need one side length, since an equilateral triangle has three equal sides.^[15]

   • For example, if a triangle has sides that are 5, 7, and 12 cm in length, you simply add up all the side lengths to find the perimeter: ${\displaystyle P=5+7+12=24}$ . So, the perimeter of the triangle is 24 cm.

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   Find the perimeter of an isosceles triangle with a missing side length. An isosceles triangle is when the height, or the altitude, bisects the base. If you know the height and base of the triangle, you can use the Pythagorean theorem to find the missing side lengths.^[17]

   • For example, if an isosceles triangle has a height of 10 cm and a base of 6 cm, you can think of the height creating two right triangles. Since the height bisects the base, one side length of the right triangle will be 3 cm. The other side length will be equal to the height: 10 cm. The missing side length is the hypotenuse.
   • Set up the Pythagorean formula, plugging in the side lengths: ${\displaystyle 10^{2}+3^{2}=c^{2}}$ .
   • Make the necessary calculations to find the missing side length:
     ${\displaystyle 100+9=c^{2}}$
     ${\displaystyle 109=c^{2}}$
     ${\displaystyle {\sqrt {109}}={\sqrt {c^{2}}}}$
     ${\displaystyle 10.44=c}$ .
   • An isosceles triangle has 2 equal sides. So, the perimeter of the triangle is equal to ${\displaystyle 2x+b}$ , where ${\displaystyle x}$ equals the length of one side, and ${\displaystyle b}$ equals the base. So, if you know the length of the base and one side, you can find the perimeter of an isosceles triangle: ${\displaystyle P=2(10.44)+6=26.88}$ . So, the perimeter of the triangle is 26.88 cm.

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   Find the length of one side. A regular polygon is a polygon that is equiangular and equilateral. You can find the length of one side if you know the length of the polygon's apothem or radius. The apothem is the distance between the center of the polygon to the midpoint of any side, and the radius is the distance between the center of the polygon and any vertex.^[18]

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   Set up the formula for the perimeter of a regular polygon. The formula is ${\displaystyle P=nx}$ , where ${\displaystyle n}$ is the number of sides the polygon has, and ${\displaystyle x}$ is the length of one side.^[21]

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   Measure the "sides" of your ellipse. An ellipse is an oval-shaped circle, so it doesn't have any straight lines. To find the perimeter, you need to know the circumference of both the height and the width, or variables a and b. If you don't know this information already, you can measure your ellipse on your own.^[23]

   • Normally, variable a goes from left to right on the major axis, and variable b goes up and down on the minor axis.

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   Plug the information into an equation. There are actually a few different equations that you can use to find the perimeter of an ellipse, and they all may give you a slightly different answer. The easiest formula to use is: ${\displaystyle p=2\pi {\sqrt {(a^{2}+b^{2})/2}}.}$ ^[24]

   • This will give you an answer within 5% of the true perimeter of the ellipse.
   • For example, if variable a is 3 and variable b is 2, your equation would look like this: ${\displaystyle p=2\pi {\sqrt {(3^{2}+2^{2})/2}}.}$

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   Solve the equation. Now you can use your inputted variables to find the perimeter of the ellipse. Remember that this is an approximate answer, not an exact one.^[25]

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   Find the length of the arc. A sector is a triangular slice taken from a whole circle (it looks like a piece of pizza). To start the equation, you need to find the length, or variable l, of the arc itself.^[26]

   • If you aren't given that information, you can solve for l with this equation: ${\displaystyle l=(\theta /360)\times 2\pi r}$ .

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   Plug the variables into the equation. To find the perimeter of a sector, plug your numbers into this equation: ${\displaystyle 2r+(\theta /360)\times 2\pi r}$ , where "2r" is 2 times the radius and "θ" is the angle of the sector. Once you've done that, you can solve for the perimeter.^[27]

   • For example, ${\displaystyle 2\times 4+(60/360)\times 2\times 3.14\times 4}$ .

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   Solve the equation. Once you've plugged in your variables, you can use the order of operations to solve for the perimeter. This is an exact number, so use the equal sign for your answer.^[28]

   • ${\displaystyle 2\times 4+(60/360)\times 2\times 3.14\times 4=12.2mm}$ .

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   Find the number of sides and the length of one side. A pentagon always has 5 sides, so you'll always be able to plug 5 into your equation. Then, all you need to find out is the length of one side to plug in for the variable.^[29]

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   Plug the variables into the equation. The formula to find the perimeter of a pentagon is ${\displaystyle P=5\times s}$ . The variable "s" stands for the length of 1 side.^[30]

   • For example, your equation might look like this: ${\displaystyle P=5\times 10}$ .

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   Solve for the perimeter. Once you've got your equation, you can use the formula to figure out the answer. Check your answer on a calculator to make sure it's right.^[31]

   • For example, ${\displaystyle P=5\times 10=50}$ .

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   Find the length of all 4 sides. A quadrilateral looks like a rectangle with uneven sides. If you know all 4 sides of the quadrilateral, you can find the perimeter by adding them all up.^[32]

   • If you don't know the length of all 4 sides, you can use the information you do have to solve for variable x.

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   Plug the side lengths into your equation. To find the perimeter of a quadrilateral, you just need to add up the side lengths. The formula is ${\displaystyle P=(a+b+c+d)}$ .^[33]

   • For example, ${\displaystyle P=5+7+9+11}$ .

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   Add up the lengths to find the perimeter. Once you know all 4 side lengths, just add them up. Don't forget to put your units on the end of your answer.^[34]

   • For example, ${\displaystyle P=5+7+9+11=32cm}$ .

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Add New Question

• Question

  If given area and length of a rectangle, how do I find the perimeter?

  

  Divide the area by the length, giving you the width. Add twice the width to twice the length.

• Question

  What's the perimeter of a triangle that has sides of 2/3, 2/5 and 2/3?

  

  Add the three sides together: 2/3 + 2/5 + 2/3 = 10/15 + 6/15 + 10/15 = 26/15 = 1 11/15.

• Question

  The perimeter of a rectangle is 64 feet. Length is 7 feet less than 2 times the width. What are the dimensions of the rectangle?

  

  Let x = the width. Then the length is 2x - 7. The perimeter is twice the width plus twice the length: 64 = (2x) + 2(2x - 7) = (2x) + (4x - 14) = 6x - 14. So 64 = 6x - 14, and 78 = 6x. Then x = 13 ft, and the length is (2)(13) - 7 = 26 - 7 = 19 ft. To check: (2)(13) + (2)(19) = 26 + 38 = 64.

• Question

  An uniunit square has its corners chopped off to from a regular polygon with eight sides. What is the area of this polygon?

  

  Split the polygon into two trapezoids and a rectangle. Find the area of the three shapes, and add them up, that's the area.

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• To find the perimeter of a trapezoid when you are missing side lengths, in general you want to divide the trapezoid into two right triangles and one rectangle. From there you can use the properties of right triangles and rectangles to find the missing side lengths.

• To find the perimeter of a rhombus when you are missing side lengths, in general you want to use the diagonal(s) of the rhombus to divide the shape into several right triangles. Then you can use the Pythagorean theorem or trigonometry to find the missing side lengths.

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The right way to find perimeter depends on the shape you're working with. For rectangles, use the formula p = 2 (w + h), where w is the width of the rectangle and h is the height. To find the perimeter of a square, use the formula p = 4x, where x is the length of 1 side of the square. If you need to find the perimeter of a triangle, use the formula p = a + b + c, where a, b, and c are the lengths of the 3 sides of the triangle. Finally, to find the perimeter of a circle, use the formula c = π (d), where c is the perimeter and d is the diameter. If you want to learn how to find the perimeter of any regular polygon, keep reading the article!

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how to find the perimeter of a circle

Source: https://www.wikihow.com/Find-Perimeter

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