MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández

7- Therefore, trapezium ABCD has an area half of the rhomboid ADGH.

8- So: area ABCD =
2

1

DG × IJ =

2

DC+AB

IJ

7.5 PROBLEMS IN THE CARTESIAN PLANE

To obtain the coordinates of point P:

AB = 4 + 1 = 5

!AOB is similar to !OPC

2

1

= =

OC

PC

x

y

P

P ; =

yP sen 2"

sen " =

5

1

; sen 2" = 2 sen " cos " =

5

4

5

1

1

5

2

− =

5

4

yP=sen 2 α= ;

5

8

xP= 2 yP=

X

To get the coordinates of point P and the area of quadrilateral OFPD.

xP= 1+AE = 1+AP sen α = 1 +4sen

(^2) α = 2,23
yP= (xP-1) / tang α = 2 3 1 , 846
1 , 23
× =
area (OFPD) = (OFA) + (AFPD) = 1 + 2 × 2 = 5
A B FHI
D ECG J
Y
OOX
Y
X O
Y
X
2
1
1
P
B
A
BC
P
2
2
" =ArTang 





3
2
!ABD≡AB=2senα
AP = 2 AB = 4sen α