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Best answer by Werner_E

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

 

1 reply

W
Werner_E25-Diamond IAnswer
25-Diamond I
December 22, 2022

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
    21-Topaz I
    ttokoro21-Topaz IAuthor
    21-Topaz I
    January 31, 2023

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    t.t.
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