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## How to solve the 12 years kids puzzle.  18-Opal

## How to solve the 12 years kids puzzle.

Find the total area of ΔABD+ΔEDC. Prime 8 sheet attached. 1 ACCEPTED SOLUTION

Accepted Solutions  24-Ruby V
(To:ttokoro) 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 😉 or this one 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: 2 REPLIES 2  24-Ruby V
(To:ttokoro) 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 😉 or this one 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:   18-Opal
(To:Werner_E)    