Grades 3-4 Video Solutions 2012-2012_3-4

Video Transcription

Problem number two. In four of the five pictures below, the white area is equal to the gray area. In which picture are the white area and the gray area different? A, B, C, D, or E?  If we look at A, we see that this white triangle has the same area as this gray triangle, and this white triangle has the same area of this gray triangle.  And then we have two dots, and their area is the same. So A cannot be the answer, because the areas are the same. In B, we see that this white triangle matches this gray triangle,  and this white part is the same as this gray part. So B cannot be the answer. In C, we have matching triangles for all corners and in the center, and we also have the dots.  So all of these have the same area,  which means C cannot be our answer. Let's look at D. Here's a close-up. So we see here that the matching parts are the same colors.  So the area of the two gray triangles is the same. The area of the two gray circles is the same. The area of the two white parts is the same.  We can't match the white to the gray like we could in the other ones. So this means that D is the answer. And at E, we see the white part is the same as this gray part,  and this white triangle is the same as this gray part. So the areas match. The only picture in which the white and the gray are different is D.

Video Summary

The problem involves determining which of five pictures has unequal white and gray areas. Analyzing pictures A, B, C, and E, the solution confirms equal areas by matching corresponding parts, such as triangles, circles, and additional shapes. However, picture D lacks such matching between white and gray areas, indicating that their areas are different. Thus, picture D is the answer where the white area and the gray area are not equal.

Keywords

unequal areas

picture analysis

geometry

area comparison

visual puzzle