Is this magic?
Geometry
Level
4
I'm a magic quadrilateral. Putting copies of me together in 2-D, I can fully cover an equilateral triangle. Putting copies of me together in 3-D, I can be the faces of a special kind of fair dice.
What quadrilateral am I?
Kite
Parallelogram
Rhombus
Square
Rectangle
Trapezoid
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1 solution
An equilateral triangle can be divided equally into 3 kites as shown above. The only other quadrilateral that can divided like that is an isosceles trapezoid; however, only kites can form a fair 10-faced die as shown below:
Such shape is called a pentagonal trapezohedron, consisting of 10 congruent kites, and so only kites fit for the answer.