You may also like

Kissing Triangles

Determine the total shaded area of the 'kissing triangles'.

Isosceles

Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. Find other pairs of non-congruent isosceles triangles which have equal areas.

Trice

ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?

Tetrahedra Tester

Age 11 to 14 Challenge Level:

What are the limitations on the lengths of the sides of any triangle?

Look at different cases.

If the base is a 4 by 5 by 6 triangle, what size can the other faces be?

How many different tetrahedra can have as its base a 4 by 5 by 6 triangle?

Can you find 8 or more possible tetrahedra?

How will you know when you have them all?