Find the perimeter of the figure.
Understand the Problem
The question asks us to find the perimeter of the figure shown in the image. To do this, we need to find the length of all the sides and then sum them together.
Answer
49 ft
Answer for screen readers
49 ft
Steps to Solve
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Identify known side lengths The following side lengths are given: $AB = 3$ ft, $EF = 3$ ft, $BC = 3$ ft, $AJ = 8$ ft, $HI = 2$ ft, $JI = 10$ ft.
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Determine the length of side CD Since $JI = 10$ ft, $IH = 2$ ft and $AB = 3$ ft, $FE = 3$ ft, we have $JI = AB + CD + EF + HI$. Therefore, $10 = 3 + CD + 3 + 2$, which gives us $CD = 10 - 3 - 3 - 2 = 2$ ft.
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Determine the length of side HG Since $AJ = 8$ ft and $BC = 3$ ft, we have $AJ = BC + HG + FE$, then $8 = 3 + HG + 3$, which means $HG = 8 - 3 - 3 = 2$ ft.
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Determine the length of side FG Since $AJ = 8$ ft, we have $FG = AJ = 8$ ft.
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Determine the length of side DE Since $AJ = 8$ ft, we have $DE = AJ = 8$ ft.
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Compute the perimeter The perimeter is the sum of all side lengths: $AB + BC + CD + DE + EF + FG + GH + HI + IJ + JA = 3 + 3 + 2 + 8 + 3 + 8 + 2 + 2 + 10 + 8 = 49$ ft.
49 ft
More Information
The perimeter of the figure is 49 ft.
Tips
A common mistake is to miss one or more sides when summing the lengths. Another common error is incorrectly calculating the length of a side using the given information. For example, if the $HI$ segment would not have been there, the $CD$ segment would be the total length of the base minus the lengths of $AB$ and $EF$.
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