tetrahedron
Geometry
Level
pending
Find the height of a tetrahedron with edges of 20m. Round to the nearest cm.
The answer is 1633.
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1 solution
A tetrahedron has equilateral triangles for faces. A vertical plane of symmetry runs through the top, and one of the other vertices, and perpendicular through the middle of the edge that connects the other two vertices. In this plane we get a new (isosceles) triangle with sides: 2 0 , 1 0 3 , 1 0 3 . The shorter sides correspond to the height of a face.
By using pythagoras and using similar triangles, we find the height, see figure