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Senior Manager
Joined: 16 Apr 2009
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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?
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Senior Manager
Joined: 25 Mar 2009
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I am calculating 12, not 24. This is also difficult to explain without a picture.
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Senior Manager
Joined: 16 Apr 2009
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I also got 12. I got all these problems from www.bellcurves.com
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Senior Manager
Joined: 04 Jun 2008
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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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Current Student
Joined: 13 Jan 2009
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Location: India
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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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Manager
Joined: 17 Dec 2007
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[1] , given: 8
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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 
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Current Student
Joined: 13 Jan 2009
Posts: 375
Location: India
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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 My bad I read it as area of triangle BCE as 48.
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Senior Manager
Joined: 16 Apr 2009
Posts: 252
Schools: Ross
Followers: 1
Kudos [?]:
10
[0], given: 10
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Thanks for the reply..
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