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What is the surface area of the triangular prism? (1 point) ___square centimeters

the w is 4cm
the L is 11cm
the H is 3cm
and theres a angle peice that is 5 cm

1 answer

To find the surface area of a triangular prism, you need to calculate the area of the two triangular bases and the three rectangular faces.

Given your dimensions:

  • Width (w): 4 cm
  • Length (L): 11 cm (the length of the prism)
  • Height (H): 3 cm (which can be interpreted as the height of the triangular base)
  • There is an additional angle piece of 5 cm (this may refer to the length of one side of the triangle or possibly the slant height).

Assuming the given values correspond as follows:

  • The triangular base is a right triangle with a height (H) of 3 cm and a base (w) of 4 cm, while the length of the prism is 11 cm.

Step 1: Area of the triangular base

The area \( A \) of a triangle is given by the formula: \[ A = \frac{1}{2} \times \text{base} \times \text{height} \] Substituting the values: \[ A = \frac{1}{2} \times 4 \text{ cm} \times 3 \text{ cm} = 6 \text{ cm}^2 \]

Step 2: Area of the two triangular bases

Since there are two triangular bases, the total area for the bases is: \[ \text{Area of bases} = 2 \times A = 2 \times 6 \text{ cm}^2 = 12 \text{ cm}^2 \]

Step 3: Area of the rectangular faces

The three rectangular faces consist of:

  1. One rectangle with dimensions of the base of the triangle (4 cm) and the length of the prism (11 cm).
  2. One rectangle with dimensions of the height of the triangle (3 cm) and the length of the prism (11 cm).
  3. One rectangle corresponding to the other side of the triangular base (which we can assume corresponds to the additional piece of 5 cm) and the length of the prism (11 cm).

Calculating each rectangular area:

  1. Rectangle 1: \[ \text{Area} = 4 \text{ cm} \times 11 \text{ cm} = 44 \text{ cm}^2 \]

  2. Rectangle 2: \[ \text{Area} = 3 \text{ cm} \times 11 \text{ cm} = 33 \text{ cm}^2 \]

  3. Rectangle 3: Assuming the side with length 5 cm: \[ \text{Area} = 5 \text{ cm} \times 11 \text{ cm} = 55 \text{ cm}^2 \]

Step 4: Total surface area

Now sum the areas of the bases and the rectangular faces: \[ \text{Total surface area} = \text{Area of bases} + \text{Area of rectangles} \] \[ = 12 \text{ cm}^2 + 44 \text{ cm}^2 + 33 \text{ cm}^2 + 55 \text{ cm}^2 = 144 \text{ cm}^2 \]

Thus, the surface area of the triangular prism is: \[ \boxed{144} \text{ square centimeters} \]