## J.L. 3 years ago PLEASE HELP! The figure below shows AB = 4 units and BD = 6 units. If the area of triangle ADE is 50 square units, what is the area of the trapezoid BCED? 40 square units 44 square units 48 square units 42 square units http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_Seg_Two_Exam_35/image0034e9d7dd7.jpg

1. Calcmathlete

Are you familiar with the concept that similar figures have a ratio for area?

2. lgbasallote

de javu

3. J.L.

Yea

4. Calcmathlete

I mean as in if there is a ratio between side lengths a : b, then the ratio fo the areas is $$a^2 : b^2$$

5. lgbasallote

im thinking area of big triangle - area of small triangle = area of trapezoid

6. J.L.

Yea I know what you're talking about @Calcmathlete

7. Calcmathlete

Yup. First you have to find the area of the smaller triangle though. If a : b is 2 : 5, then what is $$a^2 : b^2$$?

8. J.L.

4:25

9. lgbasallote

how did you get 2:5 again?

10. J.L.

Shouldn't it be 4:5?

11. Calcmathlete

The ratio of the similar triangles lgba. Now, set up a proportion between the two areas. $\frac{4}{25} = \frac{x}{50}$Solve for x.

12. Calcmathlete

Why do you say it should be 4 : 5?

13. J.L.

Because that's the ratio of the corresponding sides...CB=4 and BE=5 so the ratio would be 4:5 or 0.8

14. Calcmathlete

Are we looking at the same picture?

15. J.L.

Sorry I was looking at a different question haha

16. J.L.

shouldn't it be 4:6 then or 2:3?

17. Calcmathlete

Not quite. That isn't the ratio of the triangles. Think about it. 6 is a part of the side of a triangle. Not the actual triangle.

18. J.L.

Okay got it x=8

19. Calcmathlete

Ok. Now subtract the areas of the two triangles.

20. J.L.

I know the area of the first triangle is 50...what's the area of the second?

21. Calcmathlete

Area of the second triangle = 8

22. J.L.

Ohhh 50-8=42

23. Calcmathlete

There you go :)

24. J.L.

You are truly awesome

25. Calcmathlete

lol Thanks @lgbasallote Clearly you need to brush up on those geometry skills ;)

26. lgbasallote

...clearly...

27. lgbasallote

hmm it always is 42 huh