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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)

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