Perimeter of Parallelograms
Parallelograms are also quadrilaterals. Like rectangles, their opposite sides are congruent. The following examples model different types of parallelogram perimeter problems.
Example 1
The dimensions of a parallelogram are given next.
What is the perimeter of the parallelogram?
Read and understand the question. This question is looking for the perimeter of the parallelogram.
Make a plan. Two of the dimensions are given in the diagram. Because the figure is a parallelogram, the opposite sides are congruent. Thus, the four sides measure 4 cm, 4 cm, 8 cm, and 8 cm.
Carry out the plan. Add the sides: 4 + 4 + 8 + 8 = 24. The perimeter is 24 cm.
Check your answer. To check this solution, start with the perimeter of 24 cm. If each side length is subtracted from this value, the result should be zero: 24 – 4 – 4 – 8 – 8 = 0, so this solution is checking.
Example 2
The base of a parallelogram is four times the length of the adjacent side. If the perimeter is 120 meters, what is the length of the side adjacent to the base of the parallelogram?
Read and understand the question. This question is looking for the length of the side adjacent, or next to, the base of the parallelogram. The relationship between this side and the base is given, along with the perimeter of the parallelogram.
Make a plan. Use the relationship between the base and the adjacent side to write let statements. Then, add the four sides together and set the equation equal to 120.
Carry out the plan. Let x = adjacent side, and let 4x = base. The perimeter is x + 4x + x + 4x = 120. Simplify to get 10x = 120. Divide each side by 10 to get x = 12. The length of the side is 12 meters.
Check your answer. To check your solution, substitute x = 12 into the perimeter formula to make sure that the perimeter is equal to 120 meters. Since x = 12, 4x = 4(12) = 48 meters. Add the four sides: 12 + 48 + 12 + 48 = 120 meters. This solution is checking.
Perimeter of Squares
Squares are quadrilaterals with four equal sides. The following example solves for the perimeter of a square.
Example
A side of a square measures 7 cm. What is the perimeter?
Read and understand the question. This question is looking for the perimeter of a square.
Make a plan. The perimeter is the distance around the object. Since the figure is a square, the sides are of equal length.
Carry out the plan. Add the sides: 7 + 7 + 7 + 7 = 28. The perimeter is 28 cm.
Check your answer. To check this solution, start with the perimeter of 28 cm. If each side length is subtracted from this value, the result should be zero: 28 – 7 – 7 – 7 – 7 = 0, so this solution is checking.
Perimeter of Regular Polygons
Tip:A regular polygon is a figure whose sides are the same lengths and whose angles are all the same measures. 
The perimeter of a regular hexagon is 24 units. What is the measure of each side of the figure?
Read and understand the question. This question is looking for the perimeter of a regular hexagon.
Make a plan. The perimeter is the distance around an object. A regular hexagon is a sixsided polygon where each side has the same measure.
Carry out the plan. Since we are given the perimeter of a hexagon, and a hexagon has six sides, divide the perimeter by six to find the length of one side: = 4 units.
Check your answer. To check this solution, start with the perimeter of 24 units. If each side length is subtracted from this value, the result should be zero: 24 – 4 – 4 – 4 – 4 – 4 – 4 = 0, so this solution is checking.
Find practice problems and solutions for these concepts at Perimeter Word Problems Practice Questions.
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