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How to solve the 12 years kids puzzle.

ttokoro
20-Turquoise

How to solve the 12 years kids puzzle.

Find the total area of ΔABD+ΔEDC. Prime 8 sheet attached.

image.png

1 ACCEPTED SOLUTION

Accepted Solutions

Werner_E_2-1671714607223.png

 

A 12 year old probably should introduce point F and see, that ABD and DFE are congruent and ABD and EFC are similiar.

So we have 3 cm : 4 cm = EF : (1 cm-EF) and this yields EF=BD=3/7 cm.
Now the area of the three right angled triangles can easily be added up to 69/49 cm².

 

But if you are looking for a more elaborate Mathcad solution, you may take this one 😉

Werner_E_0-1671717392231.png

or this one

Werner_E_1-1671717410258.png

 

EDIT: Once we have determined that BD=3/7 cm by whatever method, its easier to calculate the area without using any trigonometry by calculating area of triangle ABC minus area of the half square ADE:

Werner_E_0-1671811450172.png

 

View solution in original post

2 REPLIES 2

Werner_E_2-1671714607223.png

 

A 12 year old probably should introduce point F and see, that ABD and DFE are congruent and ABD and EFC are similiar.

So we have 3 cm : 4 cm = EF : (1 cm-EF) and this yields EF=BD=3/7 cm.
Now the area of the three right angled triangles can easily be added up to 69/49 cm².

 

But if you are looking for a more elaborate Mathcad solution, you may take this one 😉

Werner_E_0-1671717392231.png

or this one

Werner_E_1-1671717410258.png

 

EDIT: Once we have determined that BD=3/7 cm by whatever method, its easier to calculate the area without using any trigonometry by calculating area of triangle ABC minus area of the half square ADE:

Werner_E_0-1671811450172.png

 

ttokoro
20-Turquoise
(To:Werner_E)

image.pngimage.pngimage.png

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