"Fun" math problem at Tech Ed
- Thread starter LoganB
- Start date
mad
LOL yeah sure
1. hold ruler to PC screen, measure known distance (10), come up with scaling factor.
2. Hold ruler to PC screen again, measure 3 sides of triangle, apply scaling factor, get side lengths.
3. head on over to http://www.mathopenref.com/heronsformula.html, plug in numbers.
4. post answer with zero explanation and revel in the fact that you're almost clever
If you ain't cheatin' you ain't tryin'
mbartoli
Member
I got 100, but I cheated... used AutoCAD. Of course, AutoCAD says that both ABCD and DEF have the same area of 100, so I am not buying it!
mbartoli
Member
So, using AutoCAD dimensions (more accurate than a ruler against the screen, I would think) and plugging these numbers into the Heron's Formula calculator
FD = 8.9443
DE = 7.0711
EF = 3.1623
It says the area is 10.0002
I can believe that, plus now I have the formula!
Thanks for sharing that!
FD = 8.9443
DE = 7.0711
EF = 3.1623
It says the area is 10.0002
I can believe that, plus now I have the formula!
Thanks for sharing that!
I also get 10 using AutoCAD.
The way to solve by hand is:
Define a new point X, which is the center (not centroid) of the semicircle, also the midpoint of AD.
Consider a quadrilateral XFCD. Angle XDC is 90, angle XFC is 90, therefore quadrilateral XFCD is symmetrical about the line XC. Angle CXD is atan(10/5), multiply that by 2 to get angle DXF.
From there, the area will be that larger sector (DXF) of the semicircle minus all the little parts, which is straightforward.
The way to solve by hand is:
Define a new point X, which is the center (not centroid) of the semicircle, also the midpoint of AD.
Consider a quadrilateral XFCD. Angle XDC is 90, angle XFC is 90, therefore quadrilateral XFCD is symmetrical about the line XC. Angle CXD is atan(10/5), multiply that by 2 to get angle DXF.
From there, the area will be that larger sector (DXF) of the semicircle minus all the little parts, which is straightforward.
I hear you, that definitely cleaned out some cobwebs in my head.
L D[AR2P#0.0]
Lifetime Supporting Member
My solution - diagram
L D[AR2P#0.0]
Lifetime Supporting Member
my solution - algebra
L D[AR2,P#0.0] I am impressed. That is why we have to learn math in school. I still prefer AutoCAD, I do better with pictures. LOL
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