To determine the total amount of fabric Keivan will need to construct his tent, we first need to calculate the area of the equilateral triangle bases and then consider the areas of the rectangles connecting the triangles.
Step 1: Area of the Equilateral Triangle Base
The formula for the area of an equilateral triangle is:
\[ \text{Area} = \frac{\sqrt{3}}{4} \times s^2 \]
where \( s \) is the length of a side of the triangle.
Given \( s = 4 , \text{ft} \):
\[ \text{Area} = \frac{\sqrt{3}}{4} \times (4)^2 \] \[ = \frac{\sqrt{3}}{4} \times 16 \] \[ = 4\sqrt{3} , \text{ft}^2 \]
Step 2: Area of the Two Triangle Bases
Since there are two triangular bases, we multiply the area of one triangle by 2:
\[ \text{Total area of two triangles} = 2 \times 4\sqrt{3} = 8\sqrt{3} , \text{ft}^2 \]
Step 3: Area of the Connecting Rectangles
Next, we need to find the area of the rectangles connecting the triangles. Let's denote the length of the rectangles by \( l \) (the problem did not provide a value for \( l \)). The height of the triangles is given as \( 2.8 , \text{ft} \).
Assuming that the rectangles connecting the bases have a width equal to the height of the triangle (this is typical for tents), the area of one rectangle can be calculated as follows:
\[ \text{Area of one rectangle} = \text{height} \times \text{length} = 2.8 , \text{ft} \times l , \text{ft}. \]
Since there are two connecting rectangles (one on each side of the triangle bases), the total area for rectangles is:
\[ \text{Total area of rectangles} = 2 \times (2.8 \times l) = 5.6l , \text{ft}^2. \]
Step 4: Total Area of Fabric
Finally, to find the total amount of fabric Keivan needs, we add the areas of the triangles and the rectangles:
\[ \text{Total Area} = 8\sqrt{3} + 5.6l , \text{ft}^2. \]
Conclusion
Keivan will need a total of \( 8\sqrt{3} + 5.6l , \text{ft}^2 \) of fabric to construct his tent, where \( l \) is the length of the rectangles connecting the bases. You would need to substitute \( l \) with a specific value in order to compute a final numerical amount of fabric required.