Question

1. 3 ft 3 ft 9 ft 3 ft

Explanation:

Step1: Identify the shape (triangular prism)

The figure is a triangular prism with a triangular base (equilateral triangle with side 3 ft) and length 9 ft.

Step2: Calculate the area of the triangular base

The area of an equilateral triangle with side \( s \) is \( \frac{\sqrt{3}}{4}s^2 \). For \( s = 3 \) ft, the area \( A_{base} = \frac{\sqrt{3}}{4} \times 3^2 = \frac{9\sqrt{3}}{4} \) square feet. But wait, maybe it's a right - angled triangle? Wait, looking at the diagram, the triangular base has sides 3 ft, 3 ft, and let's check. Wait, maybe it's an equilateral triangle or a right - angled isoceles triangle. Wait, another approach: if the triangular base is a right - angled triangle with legs 3 ft each, then the area of the base \( A_{base}=\frac{1}{2}\times base\times height=\frac{1}{2}\times3\times3 = \frac{9}{2}\) square feet.

Step3: Calculate the volume of the triangular prism

The volume of a triangular prism is given by \( V = A_{base}\times length \), where the length of the prism is 9 ft. So \( V=\frac{9}{2}\times9=\frac{81}{2} = 40.5\) cubic feet. Wait, let's confirm the base. The triangle has two sides of 3 ft and the base of 3 ft, so it's an equilateral triangle? Wait, no, if it's a triangular prism with a triangular base (equilateral triangle with side 3) and length 9. Then area of equilateral triangle is \( \frac{\sqrt{3}}{4}\times3^2=\frac{9\sqrt{3}}{4}\approx3.897 \) square feet. Then volume \( V = 3.897\times9\approx35.07 \) cubic feet. But maybe the triangle is a right - angled triangle. Let's re - examine the diagram. The dashed lines: the triangular base has vertices with sides 3, 3, and the base 3? Wait, maybe the triangular base is an equilateral triangle. Wait, the problem might have a right - angled isoceles triangle as the base. Let's assume that the triangular base is a right - angled triangle with legs of length 3 ft (since two sides are 3 ft and the angle between them is 90 degrees). Then area of base \( A=\frac{1}{2}\times3\times3 = 4.5 \) square feet. Then volume of the prism \( V=A\times length=4.5\times9 = 40.5 \) cubic feet.

Answer:

If the triangular base is a right - angled isoceles triangle, the volume is \( 40.5 \) cubic feet (or \( \frac{81}{2} \) cubic feet). If the base is an equilateral triangle, the volume is \( \frac{81\sqrt{3}}{4}\approx35.07 \) cubic feet. But based on the diagram's simplicity, it's more likely a right - angled isoceles triangle base, so the volume is \( 40.5 \) cubic feet (or \( 40\frac{1}{2} \) cubic feet).