Question

There is a picture of a square - BCAD, and then there is a triangle EAD.

B. E C



A. D
FIGURE NOT DRAWN TO SCALE
In the figure above, the perimeter of the equilateral triangle AED IS 6. What is the area of the rectangle ABCD?

A) 6
B) 4
C) 4 radical 3
D) 3 radical 3
E) 2 radical 3

Answer 1

wondering where E is.

Answer 2

clearly the base of ∆EAD is AD.
So, each of its sides has length 2.
Thus AD=2, and the area of ABCD is 2^2 = 4

Not sure what the EC is, but if you want the length, then since the altitude of ∆EAD is √3,

1^2 + (2+√3)^2 = EC^2
EC = √2+√6

Answer 3

unless, of course, E is inside ABCD. In that case,

1^2 + (2-√3)^2 = EC^2
EC = √6-√2

Answer 4

Why did you do
1^2 + ( 2+ radical3) ^2
Is that the Pythagorean theorem?
If it is why did you do
( 2+ radical3) ^2

Wouldn't it be
(Radical 3)^2 + EC = 2^2

Answer 5

Maybe. I figured EC was the hypotenuse of
∆ECF where F is the midpoint of BC -- the side parallel to AD.

If I got it wrong, then you may be right.

Though, I doubt it, since that makes EC=1.