Jesús de la Peña Hernández

8 SQUARES / TRIANGLES / VARIOUS
8.1 SQUARE WITH HALF THE AREA OF ANOTHER ONE.
8.1.1 FOLDING SOLUTIONS
Solution 1

Produce sequentially the four folds as follows:

Solution 2

Looking at the folds it ́s evident that square BCDG has half the area of square AEFH.

8.1.2 SOLUTIONS BY MEANS OF CUTS

Solution 1 (Tangran)

To build the main square using the 7 tangran figures (five right-angled isosceles triangles, one

square and one rhomboid). ∆()1 and ()2 are one half of the great triangle, and therefore make

up the square solution (to the right).

A B H

E F

C

D

(^12)
3
4
1- Fold AF.
2- H → AF; A → A. To get C.
3- EA → EA; C → C. To get CD.
4- HA → HA; C → C. To get CB.
Square ABCD has half the area of AHFE:
area AHFE = AH^2 ; area ABCD = AB^2
2 2
AC AH
AB= =
area ABCD =
2
1
2
2

AH
area AEFH
E
A
F
H B
D
G
= =

=
= =

=
C