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Senior Manager
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triangle [#permalink] New post 14 Jul 2009, 13:16
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If ABCD is a rectangle and E is the midpoint of side AD, BC is 12 and the area of the rectangle is 48, what is the area of triangle ACE?
[Reveal] Spoiler:
24

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Re: triangle [#permalink] New post 14 Jul 2009, 13:20
I am calculating 12, not 24. This is also difficult to explain without a picture.
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Re: triangle [#permalink] New post 14 Jul 2009, 13:23
I also got 12. I got all these problems from www.bellcurves.com
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Re: triangle [#permalink] New post 14 Jul 2009, 13:32
12

BC = AD = 12
AE = 6

Area = 48, thus AB = CD = 48/12 = 4

Area of triangle = base*height/2

if you imagine/draw ACE, and take AE as the base, then AB is the height of this triangle.

thus 6*4/2 = 12


24 cannot be. if 48 is total area of rectangle, then area of triangle ACB itself is 24,

Area of ACD = areaAEC + areaDCE = 24

AEC cannot be 24 anyway.
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Re: triangle [#permalink] New post 14 Jul 2009, 15:37
Area of triangle AEC=1/2*BC* height

Height=48/.5*12 ie 8

Now since AD is parallel to BC so AD=12 and since E is mid point so AE=6

Now Area of AEC=1/2*base*height
=1/2*6*8=24
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Re: triangle [#permalink] New post 14 Jul 2009, 16:50
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hemantsood wrote:
Area of triangle AEC=1/2*BC* height

Height=48/.5*12 ie 8

Now since AD is parallel to BC so AD=12 and since E is mid point so AE=6

Now Area of AEC=1/2*base*height
=1/2*6*8=24



Hi

24 may not be the answer

a rectangle can be bisected by the diagonal to form two right angle triangle of equal area, if AC bisects the rectangle , then area of ABC is 24 and Area of ACD is 24 ( sums to 48). AE is a midpoint of AD which means base of triangle ACD is halfed and hence area is halfed.

make any sense :roll:
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Re: triangle [#permalink] New post 14 Jul 2009, 19:06
alwynjoseph wrote:
hemantsood wrote:
Area of triangle AEC=1/2*BC* height

Height=48/.5*12 ie 8

Now since AD is parallel to BC so AD=12 and since E is mid point so AE=6

Now Area of AEC=1/2*base*height
=1/2*6*8=24



Hi

24 may not be the answer

a rectangle can be bisected by the diagonal to form two right angle triangle of equal area, if AC bisects the rectangle , then area of ABC is 24 and Area of ACD is 24 ( sums to 48). AE is a midpoint of AD which means base of triangle ACD is halfed and hence area is halfed.

make any sense :roll:



My bad I read it as area of triangle BCE as 48.
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Re: triangle [#permalink] New post 15 Jul 2009, 17:53
Thanks for the reply..
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Re: triangle   [#permalink] 15 Jul 2009, 17:53
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