#6 What Is The Volume It Forms?

3D Geometry

The centre shape is a unit square with equilateral triangles and trapeziums around it. The long edge is twice as long as the short ones.

What is the volume of the polyhedron that has such a net?

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Solution 1

Two of the solids can be positioned to form a regular tetrahedron as shown inside the cube. If the cube has edge length l, the tetrahedron’s volume V can be deduced by subtracting four right pyramids.

where s is the sidelength of the cube

The sought volume is

for

Therefore, the volume is

We have found our answer!

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