Grades 5-6 Video Solutions 2022-2022_5-6

Video Transcription

Question 16. The area of the square shown in the picture is 100 cm2. What is the area of the shaded figure?  The first thing we want to do is draw a vertical and a horizontal line through the middle of the large square. That results in something that looks just like this.  The shaded figure then we can determine what its value is based on how much of the smaller squares it takes up. Each one of these triangles in the shaded figure is identical.  Each triangle is one half of this larger rectangle that contains it. Each rectangle is one half of the area of the quadrant that contains it.  Each quadrant is one half of the area of the square. So, the shaded area is going to be this total area of the big square times one half times one half times one fourth times four.  So where do all these values come in? One fourth is for this quadrant. One half is to get to the rectangle. One half is to get to this individual triangle over here.  Of course, there are four triangles. Don't forget that. All four of them combined gets us to this value of 25 cm2. That is answer choice B.

Video Summary

The problem involves determining the area of a shaded region within a square of 100 cm². By dividing the large square into smaller sections using vertical and horizontal lines, it is found that the shaded region consists of identical triangles. Each triangle is half of the rectangle it is in, which itself is half of a quadrant. The process involves calculating one quarter of the quadrant area, further halved for the rectangle, then the triangle, and considering four such triangles. The total shaded area is therefore 25 cm², corresponding to answer choice B.

Keywords

shaded region

square area

identical triangles

quadrant division

area calculation