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?
Give this problem a try before jumping in for the solution!
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!
Unlock the paid post for the second solution to the problem!
Keep reading with a 7-day free trial
Subscribe to Mathematical Donuts 🍩 to keep reading this post and get 7 days of free access to the full post archives.