{"id":111306,"date":"2022-02-01T08:56:18","date_gmt":"2022-02-01T14:56:18","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=111306"},"modified":"2026-03-28T12:24:32","modified_gmt":"2026-03-28T17:24:32","slug":"perimeter","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/perimeter\/","title":{"rendered":"Perimeter Overview"},"content":{"rendered":"

Perimeter<\/strong> is defined as the total distance around a two-dimensional shape. The ability to calculate perimeter is a convenient skill to have because there are many real-world applications. For example, perimeter is used for calculating the boundary of a soccer field, the total amount of wood needed to create a picture frame, or the amount of materials needed to fence a backyard.<\/p>\n

Perimeter Sample Questions<\/a><\/div>\n

The perimeter of any polygon can be found by simply finding the sum of all of the side lengths. This is true regardless of how many sides the shape has, or how irregular the shape appears. Many polygons have perimeter formulas that can save a bit of time when calculating the sum of all side lengths. For example, the perimeter formula for a rectangle<\/a> is \\(P=2l+2w\\), where the length and width are multiplied by 2, and then added together.<\/p>\n

Similarly, the perimeter formula for a square<\/strong> is \\(P=4s\\), where s represents each side length. The perimeter formula for a circle, also known as the circumference<\/a>, is calculated as \\(C=2r\\), where \\(r\\) represents radius, and can be approximated as \\(3.14\\). These formulas will generally save you time when calculating perimeter.<\/p>\n

Having a strong foundational understanding of perimeter will also be relevant in more advanced math topics such as surface area calculations for three-dimensional solids<\/a>. For example, in order to calculate the surface area of a cylinder<\/strong> \\((SA=2rh)\\), you need to know the perimeter of the circular base of that cylinder (\\(2r\\)). Perimeter calculations are embedded into many areas of math, so it is very useful to have a solid understanding of the topic.<\/p>\n

It is common for perimeter problems to provide a shape with a few dimensions provided, and other dimensions unknown. For example, in the shape below, only four out of the six dimensions are provided. These kinds of perimeter problems are a bit more involved, but the ultimate goal is again to determine the total distance around the shape. Before calculating the perimeter, we need to identify the length of the missing side lengths. This can be done by comparing side lengths that are opposite of each other.<\/p>\n

For example, the height of the rectangle below is \\(12\\text{ mm}\\), therefore the missing side length on the right side of the figure needs to be \\(5\\text{ mm}\\) so that both heights are equal \\((12\\text{ mm}=7\\text{ mm}+5\\text{ mm})\\). The total width of the figure can be determined by adding the two partial widths \\(15\\text{ mm}+8\\text{ mm}\\), which equals \\(23\\text{ mm}\\). Now that all side lengths are accounted for, the total perimeter can be calculated. When all side lengths are added, the result is \\(70\\text{ mm}\\).<\/p>\n

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Another approach for finding the perimeter of rectangles<\/strong><\/a> with \u201cpushed-in\u201d corners is to visualize the \u201cpushed-in\u201d corner as being \u201cpushed-out\u201d to form a rectangle. When the corner is \u201cpushed-out\u201d, the perimeter remains the same, even though the area has changed. In the previous example, the \u201cpushed-out\u201d rectangle would be a \\(12\\text{ mm}\\times23\\text{ mm}\\) rectangle, which means that \\(P=2(12\\text{ mm})+2(23\\text{ mm})\\), which simplifies to \\(70\\text{ mm}\\). The approach of counting up every single side length, or the approach of \u201cpushing-out\u201d the rectangle\u2019s corner will both result in the same answer.<\/p>\n

More advanced perimeter problems might require you to \u201cpush-out\u201d more than one corner of the figure. For example, in the figure below, we can determine the perimeter by finding the measure of all of the missing side lengths, or by \u201cpushing-out\u201d the corners to create a rectangle.<\/p>\n

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Missing side lengths approach<\/h3>\n

There are three missing side lengths in the irregular figure below. The green dimension is opposite the side labeled \\(19\\text{ m}\\), so it is also \\(19\\text{ m}\\). The total height of the figure is \\(34\\text{ m}(19\\text{ m}+15\\text{ m}=34\\text{ m})\\), therefore the blue dimension is \\(34\\text{ m}-8\\text{ m}-19\\text{ m}=7\\text{ m}\\). The total width of the figure is \\(39\\text{ m}(15\\text{ m}+24\\text{ m}=39\\text{ m})\\), so the pink dimension is found by subtracting \\(39\\text{ m}-6\\text{ m}-13\\text{ m}=20\\text{ m}\\). Now that all dimensions are solved for, the perimeter can be calculated by adding up each side length. This simplifies to \\(146\\text{ m}\\).<\/p>\n

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\u201cPush-out\u201d the corners approach<\/h3>\n

When the corners of the shape are \u201cpushed-out\u201d, the dimensions of the rectangle become \\(34\\text{ m}\\times 39\\text{ m}\\). From here we can use the perimeter formula: \\(P=2(34\\text{ m})+2(39\\text{ m})\\), which simplifies to \\(146\\text{ m}\\). As you can see, when the shapes are more complex, and more irregular, the \u201cpush-out\u201d the corners approach saves time.<\/p>\n

<\/div>\n

To re-cap, when you calculate the perimeter of a two-dimensional shape, you are finding the total distance around that shape. There are a variety of techniques used for finding the perimeter of a figure, such as perimeter formulas, \u201cpushing-out\u201d the corners of a rectangle, or simply adding up each individual side length. The strategy that you choose will often depend on what information is provided within the problem.<\/p>\n

Perimeter Sample Questions<\/h2>\n

Here are a few sample questions going over perimeter.
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\n\t\t\t\t\tQuestion #1:<\/strong>\n\t\t\t\t\t

 
\nPerimeter is defined as the _________ around a two-dimensional shape. <\/p>\n<\/div>\n\t\t\t\t\t

vertex<\/div>
area<\/div>
distance<\/div>
height<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t