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)
To find the value of the height of the larger rectangle, we first need to determine the area of the two rectangles individually.
The area of the smaller rectangle is 4 meters x 3 meters = 12 square meters.
The area of the larger rectangle can be calculated by subtracting the area of the smaller rectangle from the total area of the composite figure:
Area of larger rectangle = Total area of composite figure - Area of smaller rectangle
Area of larger rectangle = 52 square meters - 12 square meters
Area of larger rectangle = 40 square meters
Now, we can find the height of the larger rectangle by dividing its total area by the length of its base:
Height of larger rectangle = Area of larger rectangle / Base length
Height of larger rectangle = 40 square meters / 8 meters
Height of larger rectangle = 5 meters
Therefore, the value in meters of the height of the larger rectangle is 5 meters.