What are the perimeters of the trapezoid?
Are their areas identical?
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What are the perimeters of the trapezoid?
Are their areas identical?
To find the solution, we begin by calculating the perimeters of each trapezoid:
For trapezoid , the sides are , , , and . Therefore, the perimeter is:
For trapezoid , the sides are , , , and . Thus, the perimeter is:
Both trapezoids have identical perimeters of . 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 , but their areas are not necessarily identical.
, not necessarily
Given the trapezoid:
What is the area?
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.
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.
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.
To compare areas, you need the height of each trapezoid (the perpendicular distance between parallel sides). The area formula is:
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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