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F and E are midpoints of AB and AD respectively. If the side of square

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F and E are midpoints of AB and AD respectively. If the side of square  [#permalink]

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New post 23 Oct 2016, 09:34
1
5
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

80% (02:12) correct 20% (02:44) wrong based on 199 sessions

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Re: F and E are midpoints of AB and AD respectively. If the side of square  [#permalink]

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New post 23 Oct 2016, 09:53
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Bunuel wrote:
Image
F and E are midpoints of AB and AD respectively. If the side of square ABCD is 8, what is the area of triangle CEF?

A. \(8\sqrt{2}\)

B. \(9\sqrt{3}\)

C. 18

D. \(16\sqrt{2}\)

E. 24

Attachment:
T7899.png


Answer E.

Area of Shaded figure = Area of Square - (Area of Triangle AEF + Area of Triangle FBC + Area of Triangle EDC )

= 8*8 - (1/2 * 4 * 4 + 1/2 * 4 * 8 + 1/2 * 4 * 8 )

= 24. Answer.
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Re: F and E are midpoints of AB and AD respectively. If the side of square  [#permalink]

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New post 23 Oct 2016, 09:55
Area of shaded region = Are of ABCD - Area of AEF - Area of DEC - Area of BCF


= 8*8 - 0.5*4*4 - 0.5*8*4 - 0.5*8*4

=24

E


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Re: F and E are midpoints of AB and AD respectively. If the side of square  [#permalink]

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New post 23 Oct 2016, 14:18
Imagine median of isosceles triangle EFC it has to bisect angle A. And the part of the diameter from angle A to line EF is 1/2 EF= 1/2 4sqrt2

Median is the height too.
diameter of square = 8aqrt 2

Height = 8sqrt - 2sqrt2 = 6sqrt2

Area = 6sqrt2* 1/2* 4 sqrt=

24


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Re: F and E are midpoints of AB and AD respectively. If the side of square  [#permalink]

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New post 27 Jan 2019, 01:30
total area of square = 64

total area of triangles; 1/2 * 4*4 +0.5*4*8+ 0.5*4*8
=> 40
64-40
=> 24
IMO E


Bunuel wrote:
Image
F and E are midpoints of AB and AD respectively. If the side of square ABCD is 8, what is the area of triangle CEF?

A. \(8\sqrt{2}\)

B. \(9\sqrt{3}\)

C. 18

D. \(16\sqrt{2}\)

E. 24

Attachment:
T7899.png
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Re: F and E are midpoints of AB and AD respectively. If the side of square  [#permalink]

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New post 27 Jan 2019, 03:32
Bunuel wrote:
Image
F and E are midpoints of AB and AD respectively. If the side of square ABCD is 8, what is the area of triangle CEF?

A. \(8\sqrt{2}\)

B. \(9\sqrt{3}\)

C. 18

D. \(16\sqrt{2}\)

E. 24

Attachment:
T7899.png


Total area =64

Now you can do one thing calculate the area of remaining 3 triangles and subtract it from total area

Just remember that the midpoints will divide the sides, into 4 & 4 each

64 - [ 1/2 * 4* 4 + 1/2 * 4 *8 + 1/2 * 8*4 ]

64 -40

24

E
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Re: F and E are midpoints of AB and AD respectively. If the side of square   [#permalink] 27 Jan 2019, 03:32
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