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=(12)(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

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)

1 answer

To find the surface area of both triangular bases of the triangular prism, we need to use the formula for the area of a triangle. The area \( A \) of a triangle can be calculated using the formula:

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

From your description, each triangular base has a base of 5 feet, and the height can be taken as the leg measuring 3.5 feet, since that is the height perpendicular to the base.

Thus, the area of one triangular base is:

\[ A = \frac{1}{2} \times 5 \times 3.5 \]

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

\[ SA = 2 \times A = 2 \times \left(\frac{1}{2} \times 5 \times 3.5\right) = 5 \times 3.5 \]

This simplifies to:

\[ SA = 17.5 \]

However, none of the presented response options correspond to the correct representation of the total surface area calculation.

Given the options presented, the most relevant formula that matches the area of the triangular bases would be:

SA = 2\(\left(\frac{1}{2}\right)\)(5)(3.5) (Which represents the area of both triangles.)

This is derived from the triangle area formula for both triangular bases. Therefore, the correct equation among the provided options is:

SA = 2\(\left(\frac{1}{2}\right)\)(5)(3.5)

(Note: Ensure you interpret \(5\) and \(3.5\) correctly as the base and height of the triangles.)