Decomposing a Regular Triangle into a Square

1.

Make regular triangle ABC , then we would find the lengh d of the square

s.t. the regular triangle & the square have same superficial measure

make D the midpoint of BC, P on ray AD s.t. 2 PD=BC

find Q on ray BC s.t. the angle AQP be a right angle, then DQ=d

2.

Since we have d, dissect the regular triangle into 2 polygon.

3.

Find a line segment perpendicular with DE & with lengh d/2

4.

by 3, we dissect the upper polygon into 2 polygon.

4.

make M the midpoint of DE, symmetry L1 by M , then we dissect the lower polygon into 2 polygon.

then we have the 4 polygon can decomposing a regular triangle into a square.