Yong Zhang, Junyao Peng, and Jiamin Wang,

Integral Triangles and Trapezoids Pairs with a Common Area and a Common Perimeter,

Forum Geometricorum, 18 (2018) 371--380.

Abstract. Using the theory of elliptic curves, we show that there are infinitely many integral right triangle and θ-integral right (resp. isosceles) trapezoid, integral isosceles triangle and θ-integral right (resp. isosceles) trapezoid, Heron triangle and θ-integral right (resp. isosceles) trapezoid pairs with a common area and a common perimeter.

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