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?
To find the height of the larger rectangle, we first need to find the height of the smaller rectangle. The height of the smaller rectangle is given as 3 meters.
Since the total area of the composite figure is 52 square meters, we can calculate the area of the smaller rectangle by multiplying its dimensions:
Area of smaller rectangle = 4 meters x 3 meters = 12 square meters
Now we can find the area of the larger rectangle by subtracting the area of the smaller rectangle from the total area of the composite figure:
Area of larger rectangle = Total area - Area of smaller rectangle
Area of larger rectangle = 52 square meters - 12 square meters
Area of larger rectangle = 40 square meters
Since we are given the width of the larger rectangle as 8 meters, we can use the area formula (area = length x width) to find the height:
40 square meters = length x 8 meters
Length of larger rectangle = 40 square meters รท 8 meters
Length of larger rectangle = 5 meters
Therefore, the height of the larger rectangle is 5 meters.