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Trapezoids: Maximizing Area

Directions: What is the greatest area you can make with a right trapezoid that has a perimeter of 46 units?



If it wasn’t a trapezoid (any quadrilateral), what would the shape be with the biggest area? What are possible dimensions of a trapezoid that has a perimeter of 46 units? How can we determine their area?



The right trapezoid with a perimeter of 46 units and the greatest area is one with a height of 12 units, bases of 8 units and of 13 units. That trapezoid has an area of 126 square units. NOTE: this assumes that a trapezoid only has one pair of parallel sides and has integer side lengths.

Source: Patrick McGowan

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