Grades 5-6 Video Solutions 2025-2025_5-6

Video Transcription

18. The shape in the diagram is made up of identical squares. Point B is halfway between points A and C. Also point D is halfway between points C and E. Maria wants to divide the  shape into two parts of equal area. Which of the points A, B, C, D, or E should she connect with a straight line to point S to do this? Pause if you want to try and solve  it. Alright, so let's just choose one of these points and see what we can come up with.  So for example, point C. If we draw a line from there to point S, we can see that we've divided the shape into two parts, but do they have equal area? Well, one thing we can notice  to make this easier to figure out is that we have this rectangle here, that this line from S to C is the diagonal of that rectangle, right? And we can see that this triangle,  the triangle over here, is in the upper part of this shape, and then the other triangle,  the one I haven't shaded, is in the bottom part. And we can see that the rest of the bottom part looks like this rectangle over here, and the rest of the top part looks like  this rectangle over here, which I will shade in a little bit. So the key thing to notice  here is that this triangle, the shaded triangle, and the white triangle over here have the same area. This line from S to C, or S to any of these points over here, if you draw  the rectangle for which that line is the diagonal, then the two triangles will be of equal area.  So it will evenly divide that part. So then all you really need to care about is this top part and this bottom part, and we need to make sure they have the same area. And  so we can see that this bottom rectangle over here will always have an area of two squares.  So we need the top one to also have an area of two squares. And we can see when that happens  if we erase this, that if we draw a line from S to E, then if we draw the rectangle around  here, and remember this part is always evenly divided, this shaded triangle over here has the same area as the white triangle over here. But notice, now this top rectangle, the one  I'm shading right now, has the same area as this white rectangle over here. So in total, this whole region, the bottom region, has the same area as this whole top region. So  the correct answer is option E.

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