# Thread: Geometry: Triangles and Trapezoids

1. ## Geometry: Triangles and Trapezoids

Hello everyone. I am really struglling with a geometry question. It's been a long time since I've had to do any maths. Hope someone ca help and explain it to me: Line df is drawn across equilateral triangle ABC, creating trapezoid AdfC. Line df is 6 cm long. Using your knowledge of geometry, determine the area of the trapezoid AdfC and explain your method. Any help will be greatly appreciated!

2. Jessica, there is not enough information given.
Are you sure you posted the complete problem?

3. If, for example, we knew the length of the base of the triangle, the height of the triangle, or the distance from the base to line df, we could find that area. But without that, we cannot determine the area of the trapezoid.

(We can determine that the little triangle cut off above df is also a right triangle. If its base is 6 cm long, the two other sides would have length 6 also, the height of that triangle would be $\sqrt{6^2- 3^2}= 3\sqrt{3}$ and so the area of the small triangle is $(1/2)(6)(3\sqrt{3})= 9\sqrt{3}$ square cm. But it is still impossible to determine the area of the trapezoid. You can just continue the two sides f and d are on as far as you like, making the trapezoid as large as you like.)

4. Originally Posted by HallsofIvy
(We can determine that the little triangle cut off above df is also a > > > right < < < triangle.
You mean the little triangle cut off above df is also an equilateral triangle.

5. Both of you Gentlemen are using "little": should be "smaller"

6. Originally Posted by Denis
Both of you > > > Gentlemen < < < are using "little": should be "smaller"
Denis, you need to be spelling that word with a little "g." Or is it a smaller "g?"

Unfortunately, I am wrong. It is "the smaller triangle," not "the little triangle."

7. Originally Posted by lookagain
Denis, you need to be spelling that word with a little "g." Or is it a smaller "g?"
Fortunately, I did not get a blank screen...
I decided to use a CAPITAL G simply to make sure I got a response from you.

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