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# In the figure above, square CDEF has area 4.

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In the figure above, square CDEF has area 4.  [#permalink]

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03 Dec 2018, 06:24
2
3
00:00

Difficulty:

15% (low)

Question Stats:

84% (01:25) correct 16% (02:50) wrong based on 79 sessions

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In the figure above, square CDEF has area 4. What is the area of △ ABF?

(A) 2$$\sqrt{2}$$
(B) 2$$\sqrt{3}$$
(C) 4
(D) 3$$\sqrt{3}$$
(E) 6

Project PS Butler : Question #56

Attachment:

ABF.JPG [ 19.41 KiB | Viewed 861 times ]

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Re: In the figure above, square CDEF has area 4.  [#permalink]

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03 Dec 2018, 09:48
2
IMO E

Triangle $$CFB$$ is a 30-60-90 triangle, therefore is side $$FB=2*\sqrt{3}$$...

Triangle $$ABF$$ is a 45-45-90 triangle (isosceles right triangle), therefore is side $$BF=AB$$ and the hypotenuse is equal to $$2*\sqrt{3}*\sqrt{2}$$

Area of $$ABF=$$ $$\frac{1}{2}*2*\sqrt{3}*2*\sqrt{3}=$$$$6$$
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Screen Shot 2018-12-03 at 18.36.52.png [ 134.78 KiB | Viewed 729 times ]

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Re: In the figure above, square CDEF has area 4.  [#permalink]

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17 Jan 2019, 11:33
Top Contributor
HKD1710 wrote:

In the figure above, square CDEF has area 4. What is the area of △ ABF?

(A) 2$$\sqrt{2}$$
(B) 2$$\sqrt{3}$$
(C) 4
(D) 3$$\sqrt{3}$$
(E) 6

Project PS Butler : Question #56

Attachment:
ABF.JPG

If the area of the square is 4, then each side has length 2

At this point, we have a special 30-60-90 right triangle. When we compare this blue triangle to the BASE 30-60-90 right triangle . . .

. . . we see that the blue triangle TWICE the size of the BASE 30-60-90 right triangle

So, These are the measurements of the blue triangle

Finally, we have special 45-45-90 right triangle.

This triangle is also an ISOSCELES triangle, so the other side ALSO has length 2√3

What is the area of △ABF?
area of a triangle = (base)(height)/2

So, area of △ABF = (2√3)(2√3)/2
= (4√9)/2
= (4)(3)/2
= 12/2
= 6

Cheers,
Brent
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Re: In the figure above, square CDEF has area 4.  [#permalink]

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10 Feb 2019, 20:20
HKD1710 wrote:

In the figure above, square CDEF has area 4. What is the area of △ ABF?

(A) 2$$\sqrt{2}$$
(B) 2$$\sqrt{3}$$
(C) 4
(D) 3$$\sqrt{3}$$
(E) 6

First let us calculate the side CF through the given area of square
side becomes 2

After this triangle CFB will be a 30 60 90 triangle

From here we can get the corresponding side FB as 2 $$\sqrt{3}$$

Now since △ ABF, is an isosceles triangle, the height and base will be equal

1/2 * 2 $$\sqrt{3}$$ * 2 $$\sqrt{3}$$

6

E
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Re: In the figure above, square CDEF has area 4.   [#permalink] 10 Feb 2019, 20:20
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