yse the image to answer the question.

An illustration shows a triangular prism. The front triangular face is visible. The right rectangular face is visible. The visible rectangular face has a width of 5 centimeters and length of 11 centimeters. The sides and edges that are not visible are indicated by dashed lines. The legs of the triangular face are labeled 3 centimeters and 4 centimeters. The hypotenuse shares the same label as the width of the visible rectangular face.

What is the surface area of the triangular prism?

(1 point)
square centimeters
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1 answer

To find the surface area of the triangular prism, we first need to determine the surface areas of the triangular base and the three rectangular faces.

Step 1: Calculate the area of the triangular base.

The triangular face is a right triangle with:

  • One leg = 3 cm
  • Other leg = 4 cm

The area of a triangle is given by the formula: Area=12×base×height In this case, we can take the legs as the base and height: Area=12×3×4=122=6 cm2

Step 2: Determine the dimensions of the prism.

The prism has:

  • Width (one side of the triangular face) = 5 cm (this is the height of the prism)
  • The length of the prism = 11 cm

Step 3: Calculate the areas of the rectangular faces.

  1. Rectangular face corresponding to the triangular base (area on the left):

    • Width = 5 cm (height of the prism),
    • Length = hypotenuse of the triangle.

    To find the hypotenuse (c) of the triangle: c=32+42=9+16=25=5 cm

    Area of this rectangular face: Arearect=width×length=5×11=55 cm2

  2. For the right rectangular face (shown in the illustration):

    • Width = 5 cm,
    • Length = length of the prism = 11 cm.

    Area: Arearect=5×11=55 cm2

  3. For the other rectangular face (side face):

    • Corresponding to the other leg of the triangle.
    • Length = 11 cm.
    • Width = 4 cm (one leg of the triangular base).

    Area: Arearect=4×11=44 cm2

Step 4: Total surface area of the prism.

Surface area (SA) of the prism includes:

  • 2 triangular bases: Total Area=2×6=12 cm2

  • 3 rectangular faces: Total Arearect=55+55+44=154 cm2

Final Calculation:

\[ \text{Total Surface Area} = \text{Total Area}{\triangle} + \text{Total Area}{\text{rect}} = 12 + 154 = 166 \text{ cm}^2 \]

Thus, the surface area of the triangular prism is 166 square centimeters.