A Rectangle Inside a Trapezoid: Area and Uniqueness

An isosceles trapezoid has parallel bases of 18 and 8 and equal legs of 13. A rectangle rests on the longer base, with its upper corners touching the sloping legs. Its perimeter is 38. What is the rectangle’s area—and can more than one rectangle satisfy these conditions? #Geometry #MathPuzzle #SimilarTriangles #Trapezoid #Rectangle #Area #Perimeter #PythagoreanTheorem #Algebra #GeometryProblem #MathTutorial