Use the image to answer the question.
A composite of two rectangles. The top rectangle is a smaller rectangle and is centered on the top width of the bottom larger rectangle. The top rectangle has a label of 4 meters on the top side, and 3 meters on the left side. The top two angles of the top rectangle have right angle marks. The bottom rectangle has a label of 8 meters on the bottom side. The distance between the right side of the top rectangle to the right side of the bottom rectangle is 2 meters. All 4 angles of the bottom rectangle have right angle marks.
The area of the composite figure is 52 square meters. What is the value in meters of the height of the larger rectangle?(1 point)
$$
Skip to navigation
To find the height of the larger rectangle, we need to determine the height of the smaller rectangle and the combined height of both rectangles.
The area of the composite figure is the sum of the areas of both rectangles.
The area of the smaller rectangle is calculated by multiplying its length and width:
Area of the smaller rectangle = 4 meters x 3 meters = 12 square meters
Let's assume the height of the larger rectangle is h meters.
The combined height of both rectangles is h + 4 meters.
The area of the larger rectangle is calculated by subtracting the area of the smaller rectangle from the total area of the composite figure:
Area of the larger rectangle = Total area - Area of the smaller rectangle
= 52 square meters - 12 square meters
= 40 square meters
The area of the larger rectangle is also calculated by multiplying its length (which is unknown) by its width (which is 8 meters):
Area of the larger rectangle = h meters x 8 meters
Since the area of the larger rectangle is 40 square meters, we can equate the two expressions for the area:
h meters x 8 meters = 40 square meters
To solve for h, we divide both sides of the equation by 8 meters:
h meters = 40 square meters / 8 meters
= 5 meters
Therefore, the height of the larger rectangle is 5 meters.