Calculate Trapezoid Perimeters: Comparing Two Shapes with 7-Unit Parallel Sides

Perimeter Calculations with Equal Parallel Sides

What are the perimeters of the trapezoid?

Are their areas identical?

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1

Understand the problem

What are the perimeters of the trapezoid?

Are their areas identical?

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2

Step-by-step solution

To find the solution, we begin by calculating the perimeters of each trapezoid:

For trapezoid AA, the sides are 44, 77, 77, and 55. Therefore, the perimeter pApA is:

pA=4+7+7+5=23 pA = 4 + 7 + 7 + 5 = 23

For trapezoid BB, the sides are 22, 77, 1111, and 33. Thus, the perimeter pBpB is:

pB=2+7+11+3=23 pB = 2 + 7 + 11 + 3 = 23

Both trapezoids have identical perimeters of 2323. However, their areas cannot be determined to be identical without information about the heights of the trapezoids. Since these are crucial for the area calculation, the equivalence of their areas cannot be concluded from available data.

Therefore, the perimeter is pA=pB=23 pA = pB = 23 , but their areas are not necessarily identical.

3

Final Answer

pA=pB=23 pA=pB=23 , not necessarily

Key Points to Remember

Essential concepts to master this topic
  • Perimeter Rule: Add all four sides of the trapezoid together
  • Technique: Identify parallel sides first: both trapezoids have 7-unit parallel sides
  • Check: Verify by adding: Trapezoid A = 4+7+7+5 = 23, Trapezoid B = 2+7+11+3 = 23 ✓

Common Mistakes

Avoid these frequent errors
  • Confusing perimeter with area calculations
    Don't try to calculate height or use area formulas when finding perimeter = wrong approach! Perimeter only needs the side lengths, not height or base measurements. Always just add the four side lengths together.

Practice Quiz

Test your knowledge with interactive questions

Given the trapezoid:

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What is the area?

FAQ

Everything you need to know about this question

Why do both trapezoids have the same perimeter even though they look different?

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Great observation! Even though the trapezoids have different shapes, the sum of their side lengths is identical. Trapezoid A: 4+7+7+5 = 23, and Trapezoid B: 2+7+11+3 = 23.

Do trapezoids with equal perimeters always have equal areas?

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No! Perimeter only depends on side lengths, while area depends on both the parallel sides and the height between them. These trapezoids could have different heights.

How can I tell which sides are parallel in a trapezoid?

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Look for sides that are marked with the same color or have parallel line symbols. In this problem, both trapezoids have parallel sides of length 7 units each.

What information would I need to compare the areas?

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To compare areas, you need the height of each trapezoid (the perpendicular distance between parallel sides). The area formula is: A=12(b1+b2)×h A = \frac{1}{2}(b_1 + b_2) \times h

Can I solve this without the diagram?

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Yes! As long as you know all four side lengths of each trapezoid. The diagram helps you visualize the shapes, but the calculation only requires adding the side lengths.

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