I wasn't able to solve this, but according to this video (click the link to see the solution; I watched the vid, so I now know the answer), a few Chinese 5th-graders solved the problem in under a minute. That in itself is a hint, by the way. If you solve the problem, leave your answer in the comments, and please show your work/reasoning.
I've gotten more stupid as I age. I could follow the explanation, but I doubt that the reputed Chinese fifth graders used the method shown. I suspect that if they did it in less than a minute, they didn't go through the formal methods shown.
ReplyDeleteBill
I was thinking something similar. The only way to solve the problem in under a minute is to have (recently) memorized the specific geometric properties relevant to this particular problem. So I suspect that the math students had just done a unit on triangles and parallelograms and had this "quickie" method fresh in their minds.
ReplyDeleteFast way, it took me more than one minute, but less than 10. And I am almost 63.
ReplyDeleteLabel all of the areas NOT in yellow:
a = the red area
b = the area below that
c = the area to the right of the red area
d = the area below 79
e = the area below 72
f = the area to right of 72
g = the area below 10
(It takes a lot longer to explain it than to label it.)
Now, use the triangle formulas A = 1/2(b + h). Also, for a parallelogram, the length of top = length of bottom, and
length of right = length of left
If you go horizontally across the figure,
there are 2 triangles whose bases are part of the top and 2 triangle whose bases are part of the bottom. The heights are the same.
So (a + b) + (72 + e + 8) = (c + 79 + d) + (f + 10 + g)
if you go vertically, there is one triangle whose base is the left side and two triangle whose base is the right side. Again, the heights are the same.
So (a + c + 72 + f) + (d + 8 + g) = (b + 79 + e + 10)
And, amazingly, all of the letters cancel out except a, the red area.
a = 9