Help finding area triangle

[darongkun]

Find sum of area triangle ABC and 2 times of triangle CDE in this picture
AD = DC

 

[Dr.Peterson]

Find sum of area triangle ABC and 2 times of triangle CDE in this picture
AD = DC

My first thought would be to solve triangle ABC (find its other sides and angle), and use the results to solve triangle CDE. Then you can use whatever formulas you have learned to find the areas.

It's possible that there is a shortcut, though I don't immediately see any.

Please tell us what you have learned (about solving triangles, finding areas, and any other formulas or theorems you think might be useful), and show your work as far as you can get. Then we will be able to work with what you know to help you solve this. We don't just give answers:

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[darongkun]

I’ve learned phythagiras, similar triangle
and basic of trigonometry.

 

[darongkun]

And heron formula

 

[Steven G]

Did you learn about the law of sines?

 

[darongkun]

I know law of sines
But i’ve learned only angle
0,30,45,60,90 degree and 37,53 degree

and not use trigono table

 

[darongkun]

This is my incompleted work.

 

[lev888]

I know law of sines
But i’ve learned only angle
0,30,45,60,90 degree and 37,53 degree

and not use trigono table

What is the law of sines?
If you know all angles and one side this law allows you to find the other 2 sides.

 

[Dr.Peterson]

This is my incompleted work.

There is some very good thinking there, which is likely part of what you are expected to do, given that they haven't taught you enough to apply the law of sines. But that seems odd to me.

Can you tell us about the context of this problem? Is it from your class? Are you currently learning trigonometry, or geometry? What topics have just been taught?

 

[darongkun]

Context is area of geometry
I’ve learned trigonometry in basic level
sin30 sin45 sin60 sin90 sin0
I know concept law of sine (self study)
But it is not in the lesson.

 

[Dr.Peterson]

Context is area of geometry
I’ve learned trigonometry in basic level
sin30 sin45 sin60 sin90 sin0
I know concept law of sine (self study)
But it is not in the lesson.

What specific topics of geometry have been recently covered? Your work shows good understanding; but I don't have any extra ideas yet, and am hoping some details from you might suggest ideas.

 

[darongkun]

I’m not sure but this is my writing lecture.
(We learn pythagoras, similar triangle, congruent triangle, basic trigonometry, but this lesson is finding area by using basic knowledge.
maybe i will use trigonometry table to calculate
sin100 sin80 sin20 degree but they are not in any lessons.

This is another exercise that i’ve finished.

sorry for my poor english
my paper written i