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

Video Transcription

6. A, B, C, D is a square with a side length of 10 cm. What is the area of the shaded part of the figure?  The first thing to notice is that the straight line passing through D and B, this diagonal of the square, is a line of symmetry for this square.  So if we flip the square across this line of symmetry, we notice that these shaded regions all correspond to unshaded regions, and the unshaded regions likewise correspond to all  the shaded regions. The area of the unshaded region therefore has to be equal to the area of the shaded region, because each of them corresponds to another one.  If that's the case, then the shaded area has to be 1 half of the total area. In this, this is a square with a side length of 10 cm, so the area is 100 cm squared, and the shaded  area, which is 1 half of that, is 1 half times 100 cm squared, which gives us 50 cm squared. The answer to the choice that is 50 is C.

Video Summary

6. A, B, C, D is a square with a side length of 10 cm. What is the area of the shaded part of the figure? The first thing to notice is that the straight line passing through D and B, this diagonal of the square, is a line of symmetry for this square. So if we flip the square across this line of symmetry, we notice that these shaded regions all correspond to unshaded regions, and the unshaded regions likewise correspond to all the shaded regions. The area of the unshaded region therefore has to be equal to the area of the shaded region, because each of them corresponds to another one. If that's the case, then the shaded area has to be 1 half of the total area. In this, this is a square with a side length of 10 cm, so the area is 100 cm squared, and the shaded area, which is 1 half of that, is 1 half times 100 cm squared, which gives us 50 cm squared. The answer to the choice that is 50 is C.

Keywords

square

area

shaded

symmetry

diagonal