What Is the Quickest Way to Find the Perimeter?
The perimeter of a polygon is the sum of the lengths of its sides. At first glance the perimeter seems easier to calculate than the area of a polygon, since addition is a simpler operation than multiplication, but in fact multiplication is usually quicker than a series of additions, so computing the perimeter of many-sided polygons can be laborious. The exact method of calculating the perimeter will depend upon the type of polygon and how much information is given. In general the following steps should yield the quickest calculations.
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Instructions
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Multiply the number of sides by the length of a side, if the polygon is a regular polygon such as a square. For example, if the polygon is a regular octagon with sides that are each 4 inches long, the perimeter of the octagon would be eight times 4 inches, or 32 inches. Regular polygons have sides that are all identical, so in this case multiplication is the most efficient method of computing the perimeter.
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Multiply the lengths of adjacent sides by two and add the products together, if the polygon is a parallelogram or similar shape in which all opposite sides are equal. If the lengths of adjacent sides of a rectangle are known to be 3 inches and 8 inches, the perimeter of the rectangle would be two times 3 inches plus two times 8 inches, or 22 inches. The total number of products to be added will be one-half the number of sides.
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Add the lengths of all the sides together, if the polygon is not regular and opposite sides are not equal. If any sides are equal, they can be grouped together to speed up the computation. If any of the sides add up to 10, they can also be grouped together.
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Tips & Warnings
If any of the side lengths are unknown, and their lengths can’t be determined through the above steps, the lengths can sometimes be found by using the Pythagorean Theorem and other geometric relationships.
References
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