Grades 5-6 Video Solutions 2024-2024_5-6

Video Transcription

Question 19. Christian has cut four small squares from the corner of the larger square, so that the remaining area is half of the area of the original square. The side lengths  of the smaller squares are shown in the diagram. What is the perimeter of the remaining shape?  First, let's calculate the area of the four cut smaller squares. 1 times 1 is 1, 2 times 2 is 4, 3 times 3 is 9, and 6 times 6 is 36. We can add these all together to get a total  cut out area of 50. The area of the original square is double that, so we multiply by 2 to get 100. This means that our original square had a side length of 10, as the square root  of 100 is 10. Now, look at these red segments that were removed from the perimeter, and these blue segments that were added to the perimeter. Notice how they are both the same  length, which means that cutting out the square did not change the perimeter at all. We can see that this is the same for the other three cut out squares. Therefore, the perimeter  of this new shape is equal to the perimeter of the original square. We can find the perimeter of the original square by multiplying the side length, 10, by 4 to get 40. Since the  perimeter of the remaining shape is equal to the perimeter of the original square, we know that the perimeter of the remaining shape is also 40.

Video Summary

Christian cuts four smaller squares from a larger square, leaving the remaining area at half of the original. The cut areas total 50, indicating an original square area of 100, thus having a side length of 10 (since \( \sqrt{100} = 10 \)). Despite removing parts of the square, the perimeter remains unchanged because the length of cut sections and added sections are equal. The original square's perimeter is calculated as \( 4 \times 10 = 40 \). Therefore, the perimeter of the remaining shape is also 40.

Keywords

geometry

square

perimeter

area

math problem