Question: Find the total surface area of this triangular prism. [Diagram of a triangular prism with…

Find the total surface area of this triangular prism.

[Diagram of a triangular prism with dimensions labeled]

• Base of the triangular face: 5 cm
• Height of the triangular face: 12 cm
• Length of the prism: 30 cm
• Length of the slant height of the triangular face: 13 cm
• Length of the other slant height of the triangular face: 20 cm
• Length of the base of the rectangular face: 16 cm

Not to scale

Answer: \(\boxed{\text{cm}^2}\)

Solution

To find the total surface area of the triangular prism, we’ll follow these steps: Step 1: Calculate the area of the triangular base. \[ \text{Area}{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 21 \, \text{cm} \times 12 \, \text{cm} = 126 \, \text{cm}^2 \] Step 2: Determine the perimeter of the triangular base. \[ \text{Perimeter}{\text{triangle}} = 21 \, \text{cm} + 13 \, \text{cm} + 20 \, \text{cm} = 54 \, \text{cm} \] Step 3: Calculate the lateral surface area of the prism. \[ \text{Lateral Surface Area} = \text{Perimeter}{\text{triangle}} \times \text{Length} = 54 \, \text{cm} \times 30 \, \text{cm} = 1620 \, \text{cm}^2 \] Step 4: Find the total surface area by adding the areas of the two triangular bases and the lateral surface area. \[ \text{Total Surface Area} = 2 \times \text{Area}{\text{triangle}} + \text{Lateral Surface Area} = 2 \times 126 \, \text{cm}^2 + 1620 \, \text{cm}^2 = 1872 \, \text{cm}^2 \] Answer: The total surface area of the triangular prism is \(1872 \, \text{cm}^2\).