Calculate Parallelogram Perimeter: Given Area 75 cm² and Height 5 units

Parallelogram Perimeter with Insufficient Information

Look at the parallelogram in the figure below.

If its area is 75 cm², then what is its perimeter?

151515555AAABBBCCCDDDEEE

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the perimeter of the parallelogram
00:03 Opposite sides are equal in a parallelogram
00:16 The perimeter of the parallelogram equals the sum of its sides
00:26 We don't have enough data to know anything about the pair of sides AB,DC
00:30 Therefore it cannot be solved
00:33 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the parallelogram in the figure below.

If its area is 75 cm², then what is its perimeter?

151515555AAABBBCCCDDDEEE

2

Step-by-step solution

To solve this problem, we aim to find the perimeter given only the area and a side of the parallelogram. The key formula for a parallelogram’s area is Area=Base×Height \text{Area} = \text{Base} \times \text{Height} . The perimeter of the parallelogram is calculated as 2×(Base+Side) 2 \times (\text{Base} + \text{Side}) .

However, the problem only provides the area and one side length and lacks information about the height or the other side. This shortage of detail restricts us from precisely determining other necessary values, like the base and the height, critical for calculating the perimeter.

Without assuming or being provided additional information, such as the height of the parallelogram or the lengths of both pairs of opposite sides, the problem lacks sufficient detail for solving explicitly. Consequently, it is impossible to calculate the perimeter from the given information alone.

Therefore, the correct conclusion is that the perimeter calculation cannot proceed with the available data.

It is not possible to calculate.

3

Final Answer

It is not possible to calculate.

Key Points to Remember

Essential concepts to master this topic
  • Perimeter Formula: Sum of all four sides: 2×(Base+Side) 2 \times (\text{Base} + \text{Side})
  • Area Formula: Area=Base×Height \text{Area} = \text{Base} \times \text{Height} gives us 75 = Base × Height
  • Check Information: Need both base and adjacent side lengths to find perimeter ✓

Common Mistakes

Avoid these frequent errors
  • Assuming the height equals the side length
    Don't confuse the perpendicular height (5 units) with the slanted side length = wrong perimeter calculation! The height is perpendicular distance between parallel sides, not the actual side. Always identify what measurements represent actual sides versus perpendicular distances.

Practice Quiz

Test your knowledge with interactive questions

A parallelogram has a length equal to 6 cm and a height equal to 4.5 cm.

Calculate the area of the parallelogram.

6664.54.54.5

FAQ

Everything you need to know about this question

Why can't I use the height to find the perimeter?

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The height is the perpendicular distance between parallel sides, not the actual side length! The slanted sides are longer than the height. You need the actual side measurements for perimeter.

Can I find the base from the area?

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Yes! Using Area=Base×Height \text{Area} = \text{Base} \times \text{Height} , we get 75=Base×5 75 = \text{Base} \times 5 , so Base = 15 cm. But we still need the adjacent side length for perimeter.

What information would I need to solve this?

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You'd need both pairs of opposite sides or one complete side and the angle. The diagram shows side BC = 15, but we don't know the length of the slanted sides AB or CD.

Is there ever a case where this would be solvable?

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Yes! If this were a rectangle (where height equals side length) or if we had the angle information, we could calculate the missing side. But with a general parallelogram, we need more data.

How do I recognize when a geometry problem is unsolvable?

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Count your unknowns! For perimeter, you need all side lengths. If you can't determine them from the given information, the problem lacks sufficient data. Always check what's given versus what's needed.

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