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

Video Transcription

Question 22. The diagram shows four touching rectangles. What is the area of this shaded rectangle?  First, let's look at the red rectangle. We know that it has an area of 45 square centimeters and a width of 5 centimeters.  We can find the height by dividing the area by the width. We will get a height of 9 centimeters.  Now, let's look at the orange line segment. We can see that it is the difference between the red segment and the entire height. Calculating this difference gives us 4 centimeters.  Now, let's look at this yellow rectangle. We know that it has an area of 40 square centimeters and a height of 4 centimeters.  We can find its width by dividing the area by the height, giving us a width of 10 centimeters.  Now, we look at the white line segment. We can see that it is the difference between the yellow segment and the entire width. Calculating this difference gives us 6 centimeters.  Now, let's look at the blue rectangle. We know that it has an area of 48 square centimeters and a width of 6 centimeters.  We can find the height by dividing the area by the width, which gives us a height of 8 centimeters.  Since opposite sides of rectangles have the same length, we know that the top side of the yellow rectangle is 10 centimeters long,  and the bottom side of the red rectangle is 5 centimeters long. We can see that the green segment, the width of the shaded rectangle, is the difference between these two values.  Calculating this gives us a width of 5 centimeters. Using the same principle as last time, we know that the left side of the blue rectangle is 8 centimeters,  and the right side of the yellow rectangle is 4 centimeters. The teal segment, which is the height of the shaded rectangle, is the difference between the two.  8 minus 4 is 4 centimeters. Now that we know the width and the height of the shaded rectangle, we can multiply them together to get an area of 20 square centimeters.

Video Summary

The solution calculates the area of a shaded rectangle within a diagram of touching rectangles. First, by identifying and analyzing adjacent rectangles, the red rectangle's height is determined to be 9 cm using its given area and width. Then, the yellow rectangle's width is calculated as 10 cm. Further calculations reveal a 6 cm width for the white segment. For the blue rectangle, with a width of 6 cm, the height is found to be 8 cm. Applying these measurements, the shaded rectangle's dimensions (5 cm width and 4 cm height) are determined, leading to an area of 20 square centimeters.

Keywords

shaded rectangle

area calculation

geometry

touching rectangles

diagram analysis