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Resources tagged with Tetrahedra similar to Cheese Cutting:

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Broad Topics > 3D Geometry, Shape and Space > Tetrahedra

Sliced

Stage: 4 Challenge Level:

An irregular tetrahedron has two opposite sides the same length a and the line joining their midpoints is perpendicular to these two edges and is of length b. What is the volume of the tetrahedron?

Interpenetrating Solids

Stage: 5 Challenge Level:

This problem provides training in visualisation and representation of 3D shapes. You will need to imagine rotating cubes, squashing cubes and even superimposing cubes!

Four Points on a Cube

Stage: 5 Challenge Level:

What is the surface area of the tetrahedron with one vertex at O the vertex of a unit cube and the other vertices at the centres of the faces of the cube not containing O?

Tet-trouble

Stage: 4 Challenge Level:

Show that is it impossible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units...

Qqq..cubed

Stage: 4 Challenge Level:

It is known that the area of the largest equilateral triangular section of a cube is 140sq cm. What is the side length of the cube? The distances between the centres of two adjacent faces of. . . .

Classifying Solids Using Angle Deficiency

Stage: 3 and 4 Challenge Level:

Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry

Reach for Polydron

Stage: 5 Challenge Level:

A tetrahedron has two identical equilateral triangles faces, of side length 1 unit. The other two faces are right angled isosceles triangles. Find the exact volume of the tetrahedron.

Investigating Solids with Face-transitivity

Stage: 4 and 5

In this article, we look at solids constructed using symmetries of their faces.

Paper Folding - Models of the Platonic Solids

Stage: 2, 3 and 4

A description of how to make the five Platonic solids out of paper.

Tetra Perp

Stage: 5 Challenge Level:

Show that the edges AD and BC of a tetrahedron ABCD are mutually perpendicular when: AB²+CD² = AC²+BD².

Tetra Inequalities

Stage: 5 Challenge Level:

Prove that in every tetrahedron there is a vertex such that the three edges meeting there have lengths which could be the sides of a triangle.

Pythagoras for a Tetrahedron

Stage: 5 Challenge Level:

In a right-angled tetrahedron prove that the sum of the squares of the areas of the 3 faces in mutually perpendicular planes equals the square of the area of the sloping face. A generalisation. . . .

Bond Angles

Stage: 5 Challenge Level:

Think about the bond angles occurring in a simple tetrahedral molecule and ammonia.