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=2(12)(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=2(12)(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=12(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=(12)(5)(6.5)

1 answer

To find the surface area (SA) of both triangular bases of the net of the triangular prism, we can use the formula for the area of a triangle:

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

In this case, the base of the triangle is given as 5.5 feet (the base of the triangle) and the height is 3.5 feet (the height of the triangle).

The total area for both triangular bases would be:

\[ SA = 2 \times \left( \frac{1}{2} \times \text{base} \times \text{height} \right) \]

Substituting the values we have:

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

This simplifies to:

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

Thus, the correct expression for the surface area of both triangular bases is:

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

So, the correct response is:

\[ \text{upper S upper A equals 2 left parenthesis Start Fraction 1 over 2 End Fraction right parenthesis left parenthesis 5.5 right parenthesis left parenthesis 3.5 right parenthesis} \]