SOLUTION: https://vle.mathswatch.co.uk/images/questions/question2399.png. please I need help with this hard problem :) thanks

Question 1125383: https://vle.mathswatch.co.uk/images/questions/question2399.png. please I need help with this hard problem :) thanks
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

here you have right angle triangles, and
the area o the trapezium is equal to the difference of the area of and

the ->as you can see, we need to find
since and are triangles, sides are ; so, we have
...solve for

and the
the

finally,the area o the trapezium

Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

Triangles BCD and ACE are similar.

The ratio of BD:CD is 6:8 = 3:4; so the ratio of AE:CE must be 3:4.

Then, since AE=9, CE=12.

Then since you know CD=8, you know the length of DE, which is the altitude of the trapezium.

And then the area of the trapezium is the height times the average of the two bases.
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