Question

The figure above represents a window, with the shaded regions representing openings for glass and the pale regions representing the wood panels between and around the glass. If the window is 4.5 feet high by 2.5 feet wide, and if each of the wooden panels is exactly 4 inches thick, what is the total surface area, in square inches, of glass in the window?

• A. 189
• B. 378
• C. 448
• D. 756
• E. 1,620

Hint:

When calculating areas of objects with openings, subtract the area of the material from the total area to find the area of the opening.

Answer 1

The Correct Option is B

Step 1: Convert the dimensions of the window into inches.
The window is 4.5 feet high and 2.5 feet wide. Since 1 foot = 12 inches, we convert the dimensions to inches: \[ \text{Height} = 4.5 \times 12 = 54 \, \text{inches}, \quad \text{Width} = 2.5 \times 12 = 30 \, \text{inches}. \] Step 2: Calculate the total area of the window.
The total area of the window is: \[ \text{Total area of the window} = 54 \times 30 = 1,620 \, \text{square inches}. \] Step 3: Calculate the area of the wood panels.
The window has four wooden panels, one on each side of the glass. Each panel is 4 inches thick, so the dimensions of each panel are: \[ \text{Height of each panel} = 54 \, \text{inches}, \quad \text{Width of each panel} = 4 \, \text{inches}. \] Thus, the area of each panel is: \[ \text{Area of each panel} = 54 \times 4 = 216 \, \text{square inches}. \] Since there are four panels, the total area of the panels is: \[ \text{Total area of panels} = 4 \times 216 = 864 \, \text{square inches}. \] Step 4: Calculate the area of glass.
The area of the glass is the total area of the window minus the area of the panels: \[ \text{Area of glass} = 1,620 - 864 = 756 \, \text{square inches}. \] Conclusion:
Thus, the total surface area of glass in the window is 756 square inches. The correct answer is (D) 756.