Use the image to answer the question.



An illustration shows a 2 D net of a triangular prism with all of its sides open and visible. Dimensions are labeled. The parts that are not visible in 3 D view are marked with dashed lines. It appears as three vertical rectangles placed vertically. The length and width of the top rectangle are 6.5 feet and 5 feet respectively. The length and width of the middle rectangle are 5.5 feet and 5 feet respectively. The length of the bottom rectangle is 5 feet. Two identical triangles adjoin the middle rectangle on both sides with legs measuring 3.5 feet and 5.5 feet. The hypotenuse measures 6.5 feet.

Write an equation for the surface area of both triangular bases of the net.

(1 point)
Responses

SA=1/2(3.5)(5)
upper S upper A equals Start Fraction 1 over 2 End Fraction left parenthesis 3.5 right parenthesis left parenthesis 5 right parenthesis

SA=2(1/2)(3.5)(5.5)
upper S upper A equals 2 left parenthesis Start Fraction 1 over 2 End Fraction right parenthesis left parenthesis 3.5 right parenthesis left parenthesis 5.5 right parenthesis

SA=2(1/2)(6.1)(3.5)
upper S upper A equals 2 left parenthesis Start Fraction 1 over 2 End Fraction right parenthesis left parenthesis 6.1 right parenthesis left parenthesis 3.5 right parenthesis

SA=(1/2)(5)(6.5)
upper S upper A equals left parenthesis Start Fraction 1 over 2 End Fraction right parenthesis left parenthesis 5 right parenthesis left parenthesis 6.5 right parenthesis
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1 answer

To find the surface area of both triangular bases of the net, we need to use the formula for the area of a triangle, which is:

\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]

From the description, each triangular base has a base of 5.5 feet (as indicated by the dimensions of the rectangles to which the triangles are attached) and a height of 3.5 feet (one of the legs of the triangle).

So the area \( A \) of one triangle can be calculated as follows:

\[ A = \frac{1}{2} \times 5.5 \times 3.5 \]

Since there are two identical triangular bases, the total surface area \( SA \) of both triangular bases would be:

\[ SA = 2 \times \left(\frac{1}{2} \times 5.5 \times 3.5\right) = \frac{1}{2} \times 2 \times 5.5 \times 3.5 = 5.5 \times 3.5 \]

Finally, we can express this as:

\[ SA = 2 \left(\frac{1}{2} (5.5)(3.5)\right) \]

However, the correct choice from your responses would be based on the dimensions provided for the triangle, which matches the equation:

\[ SA = 2\left(\frac{1}{2}(3.5)(5.5)\right) \]

So the correct answer is:

\[ SA=2\left(\frac{1}{2}(3.5)(5.5)\right) \]