A tent is shaped like a triangular prism. Each end of the tent is an equilateral triangle with side length 4 feet. The tent is 9 feet long. Determine the surface area of the tent, not including the bottom.

To find the surface area of the tent, we first calculate the area of the two triangular ends. For an equilateral triangle with side length \( s = 4 \) feet, the area \( A \) can be calculated using the formula: \[ A = \frac{\sqrt{3}}{4} s^2 = \frac{\sqrt{3}}{4} (4)^2 = \frac{\sqrt{3}}{4} \times 16 = 4\sqrt{3} \text{ square feet} \] Since there are two triangular ends, their combined area is: \[ 2 \times 4\sqrt{3} = 8\sqrt{3} \text{ square feet} \] Next, we calculate the area of the three rectangular sides. The length of the tent is 9 feet, and the height of each rectangle (the height of the triangular end) needs to be found. The height \( h \) of an equilateral triangle can be calculated as follows: \[ h = \frac{\sqrt{3}}{2} s = \frac{\sqrt{3}}{2} \times 4 = 2\sqrt{3} \text{ feet} \] The areas of the three rectangles are: 1. Two rectangles with dimensions \( 9 \) feet by \( 4 \) feet (the base of the triangular ends): \[ A_1 = 2 \times (9 \times 4) = 2 \times 36 = 72 \text{ square feet} \] 2. One rectangle with dimensions \( 9 \) feet by \( 2\sqrt{3} \) feet (the height of the triangular ends): \[ A_2 = 9 \times 2\sqrt{3} = 18\sqrt{3} \text{ square feet} \] Now add all the areas together to find the total surface area: \[ \text{Total Surface Area} = A_{\text{triangles}} + A_{\text{rectangles}} = 8\sqrt{3} + 72 + 18\sqrt{3} \] Combining the \( \sqrt{3} \) terms: \[ = (8\sqrt{3} + 18\sqrt{3}) + 72 = 26\sqrt{3} + 72 \text{ square feet} \] Thus, the surface area of the tent, not including the bottom, is: \[ \boxed{26\sqrt{3} + 72} \text{ square feet} \]