Ten matchsticks are arranged into the shape of a wigwam. The grid is shown for your convenience only.
Providing no damaging, loose ends and overlapping of the matchsticks are allowed, it is possible to divide the wigwam shape into two parts of the same area with just two matchsticks.
True or False?
TRUE.
The shape of wigwam consists of 8 equilateral triangles. Thus, the area of each of the two parts should be equal 4 equilateral triangles. An equilateral triangle is 1/2 of a rhombus – shape A. No matter how the same rhombus is divided in half, each time its half always equals the area of the respective equilateral triangle. Thus, the half of shape B = half of shape A, i.e. = equilateral triangle.
As a result the wigwam should be divided into two parts of the same area as is shown in the illustration. The shaded part consists of three equilateral triangles and a triangle obtained from the 1/2 division in shape B. The remaining white part consists of 4 equilateral triangles as well: 8 minus 4.