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 area of the composite figure is 52 square meters. What is the value in meters of the height of the larger rectangle?

1 answer

To find the height of the larger rectangle given that the area of the composite figure is 52 square meters, we need additional information about the dimensions of both rectangles, specifically their widths and heights.

However, assuming the area of the composite figure (the larger rectangle plus the smaller rectangle) is given and we only know that this total area equals 52 square meters, we can set up an equation if we have the dimensions.

Let's denote:

  • The width of the larger rectangle as \( W_L \)
  • The height of the larger rectangle as \( H_L \)
  • The width of the smaller rectangle as \( W_S \)
  • The height of the smaller rectangle as \( H_S \)

The area of the larger rectangle is: \[ \text{Area}_{L} = W_L \times H_L \]

The area of the smaller rectangle is: \[ \text{Area}_{S} = W_S \times H_S \]

Given that the total area is: \[ \text{Area}{L} + \text{Area}{S} = 52 \]

If you provide the widths or another key relationship between the heights and widths of either rectangle, I can help solve for \( H_L \) or any other required dimensions. Otherwise, please specify any additional constraints or details available in the image for a more accurate answer.