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

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Math Expert
Joined: 02 Sep 2009
Posts: 48044
F and E are midpoints of AB and AD respectively. If the side of square  [#permalink]

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23 Oct 2016, 09:34
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4
00:00

Difficulty:

25% (medium)

Question Stats:

73% (01:54) correct 27% (01:26) wrong based on 123 sessions

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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 [ 4.34 KiB | Viewed 6812 times ]

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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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23 Oct 2016, 09:53
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Bunuel wrote:

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

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 )

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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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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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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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14 Jul 2018, 11:25
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Re: F and E are midpoints of AB and AD respectively. If the side of square &nbs [#permalink] 14 Jul 2018, 11:25
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