Due Nov 15th
What happened? Why is there an extra space?
I would suggest that you grab some graph paper and try it yourself. Your task is to explain why there is an extra space when the colored area blocks are moved. You can support your statement with an illustration if you want but you must write out an explanation. If you support your argument with an illustration bring it to me so I can post it, it might help us make sense of the problem.
Good Luck
Ms. L.
SOLUTION:
As we have discussed in class. You can not eyeball and answer a geometry problem and this is a prime example. Here is what happened in this problem:
The key to the puzzle is the fact that neither of the 13×5 "triangles" Are a triangle. Because of the measures Is what appears to be the hypotenuse, is actually bent. In other words, the "hypotenuse" does not maintain a consistent slope, even though it may appear that way to the human eye.
A true 13×5 triangle cannot be created from the given component parts. The four figures (the yellow, red, blue and green shapes) total 32 units of area. The apparent triangles formed from the figures are 13 units wide and 5 units tall, so it appears that the area should be S = 13×5/2 = 32.5 units.
So as well as the hypotenuse being bent the areas are not the same. Here is a visual to help you think about what is happening here.
RB: there is an extra space because they moved the shapes into a spot that the blocks did not fully cover
ReplyDeleteJD - per 1 when we replace the blue triangle with the red triangle, we get a space because the red triangle is way bigger than the blue one and covers a certain amount of space, so when replaced that space is not covered anymore. The red triangle is the biggest shape that's in the area which is why when replaced the space is not covered anymore
ReplyDeletebecause they left spaces open and the blocks cover up the other half
ReplyDeleteD.B.T Per1: There's an extra unit square because the rearranged figures cause a new area to be formed.
ReplyDeleteAA period:3
ReplyDeleteI believe there is an extra space because, as we see when the shape are together originally some parts of the triangles don't make up a full square. When the shapes are then moved around that is showed through the missing square piece.
I think its because how a shape is arranged can affect the mass and area of said shape. MC Period 3
ReplyDeleteAK per 3 There is a space missing because the shapes are not congruent so they do not line up with each other so therefore they did not all fit.
ReplyDeleteI think that the way the shape is formed and placed can effect the area of how all the shapes are when moved. HK Per3
ReplyDeleteNov 18 JF P1.
ReplyDeleteThe reason there is a box left over when box yellow translates over is because the blue triangle was a bit smaller than the red box. So the blue box has more space. The yellow box translates over three, down two. Therefore leaving a space between the yellow box and green box