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# How to Find the Perimeter of an Irregular Shape Without a Ruler

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## Parallel Side Method

• 1). Use the parallel side method when the irregular shape has right-angled sides of unknown dimension.

• 2). Label the sides of the shape that are parallel to each other. There will be two groups -- the horizontal sides and the vertical sides. These can either be labeled horizontal and vertical or "A" and "B," or go over the lines in two, different colored pens or pencils to indicate which are horizontal and which are vertical.

• 3). Find out the length of the longest sides. On easier examples, the length of the longest side will already be given. On more complicated examples, the length of the longest side will need to be worked out by adding up the total of the smaller parts grouped together in the vertical and horizontal groups.

• 4). Create an equation for each of the sets of parallel sides so the answer is the length of one of the long sides. This will be the sum of the component parts of that parallel group, with one of the component parts unknown (this unknown part will be "x" in the equation). For example: x+5+2=10.

• 5). Rearrange the equation by moving the known sides over to the answer side of the equation and subtracting them from the length of the long side. Working on the equation from the previous step x=10-2-5, so x=3.

## Component Shapes Method

• 1). Use this method if the unknown side of the shape is at an angle (on a slant).

• 2). Break up the shape into its component shapes. If the irregular shape has four straight edges at right angles and one short, slanted side, then it can be broken down into two, smaller rectangles and a triangle so the distance needed is part of a triangle rather than an irregular shape. At this point none of the dimensions of the triangle will be known.

• 3). Work out the dimensions of the two sides of the triangle connected by the right angle using the parallel sides method explained in Section 1.

• 4). Use the Pythagorean theorem to work out the missing side of the triangle -- A squared + B squared = C squared. If the known sides of the triangle are 4 and 3 (the "A" and the "B" of the equation), then the equation reads 16+9=C squared. The length of C is therefore the square root of 25, which is 5.