Hello My Lovely Students,

Explore the idea that all tetrahedrons with the same side lengths have the same surface area.

Ms. Tiffany

Look at the tetrahedron with side lengths 5.00, 6.00, 7.00, 8.00, 9.00, and 10.00 centimeters. Construct the tetrahedron using Cabri 3-D or by hand. Use the tool on Cabri to calculate surface area.

Tetrahedron #1:

Tetrahedron #2:

Despite having the same edge lengths tetrahedron #1 and #2 have different surface areas. Why might this be? Later on we will determine how many unique tetrahedrons can be made with side length 5, 6, 7, 8, 9, and 10. However, the overall surface area of a tetrahedron is simply the sum of the area of its triangular faces. Therefore, the construction of different triangular faces will lead to varying areas. Use Heron's formula to calculate the exact surface area of tetrahedrons #1 and #2 depicted above.