Triangles

problem

Isosceles

Age

11 to 14

Challenge level

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.
problem

Trice

Age

11 to 14

Challenge level

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?
problem

Pareq Calc

Age

14 to 16

Challenge level

Triangle ABC is an equilateral triangle with three parallel lines going through the vertices. Calculate the length of the sides of the triangle if the perpendicular distances between the parallel lines are 1 unit and 2 units.
problem

Circumnavigation

Age

14 to 16

Challenge level

The sides of a triangle are 25, 39 and 40 units of length. Find the diameter of the circumscribed circle.
problem

Half a Triangle

Age

14 to 16

Challenge level

Construct a line parallel to one side of a triangle so that the triangle is divided into two equal areas.
problem

Seven Sticks

Age

5 to 7

Challenge level

Explore the triangles that can be made with seven sticks of the same length.
problem

Three Fingers and a Loop of String

Age

5 to 7

Challenge level

Using a loop of string stretched around three of your fingers, what different triangles can you make? Draw them and sort them into groups.
problem

Board Block

Age

5 to 7

Challenge level

Take it in turns to make a triangle on the pegboard. Can you block your opponent?
problem

Logic Block Collections

Age

5 to 7

Challenge level

What do you think is the same about these two Logic Blocks? What others do you think go with them in the set?
game

Board Block for Two

Age

5 to 7

Challenge level

Board Block game for two. Can you stop your partner from being able to make a shape on the board?