To find the height of the larger rectangle, we need to understand the relationship between the areas of the rectangles and any given dimensions.
Since the problem states the total area of the composite figure is 52 square meters, we can denote the dimensions of the larger rectangle as \( l \) for the length and \( h \) for the height. The area of the larger rectangle would then be \( A_1 = l \times h \).
Given that the composite figure includes a smaller rectangle on top, we need to denote its dimensions as well, say \( l_s \) for its length and \( h_s \) for its height. Its area would then be \( A_2 = l_s \times h_s \).
The total area of the composite figure is the sum of the areas of the two rectangles: \[ A_1 + A_2 = 52 \]
For the exact values, we would need specific dimensions of at least one rectangle to proceed with a calculation.
Since we do not have specific dimensions or another equation, let's assume some general values or relationships:
- If \( l_s \) and \( h_s \) are related to the size of the larger rectangle,
- Assume simple values for \( l \) and \( h \) that abide by area constraints.
If we say, for instance, the height of the larger rectangle \( h = 4 , \text{meters} \) and its length \( l = 10 , \text{meters} \), that gives: \[ A_1 = 10 \times 4 = 40 , \text{square meters} \] Then for the smaller rectangle, we could set: \[ A_2 = 52 - 40 = 12 , \text{square meters} \] However, without specific lengths or a known ratio, it's not calculable directly.
If you provide more specific lengths, we could then use the relationship to determine the respective heights or adjust to suit the total area!
To summarize, without specific dimensions provided for both rectangles or another relationship, we cannot compute the height of the larger rectangle definitively. If further details are shared, a clear answer could be given efficiently. Please supply values or a possible ratio to pinpoint the area differences.