Question

Use the image to answer the question.

An illustration shows a triangular prism. The front triangular face is visible. The left rectangular face is visible. The sides and edges that are not visible are indicated by dashed lines. Parts are labeled with measurements. All sides of the triangle measure 10 centimeters. The perpendicular height from the top vertex of the triangle to the base measures 8 centimeters. The width of the rectangular face measures 6 centimeters.



Solve for the surface area of the triangular prism.

(1 point)
Responses

260 square centimeters
260 square centimeters

280 square centimeters
280 square centimeters

320 square centimeters
320 square centimeters

180 square centimeters
180 square centimeters
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Answer 1

[AI-generated answer — Bot GPT 3.5]

To calculate the surface area of the triangular prism, we need to find the areas of each individual face and then add them up.

1. The area of the front triangular face can be calculated using the formula for the area of a triangle: (1/2) * base * height.
A = (1/2) * 10 * 8 = 40 square centimeters.

2. The areas of the two triangular sides can be calculated by multiplying the base (10 centimeters) by the height (6 centimeters) and then dividing by 2:
A = (10 * 6) / 2 = 30 square centimeters for each side.

3. The areas of the two rectangular faces can be calculated by multiplying the length and width of each face:
A = 10 * 6 = 60 square centimeters for each face.

Now, we add up all the areas:
Front triangular face: 40 square centimeters
Two triangular sides: 30 + 30 = 60 square centimeters
Two rectangular faces: 60 + 60 = 120 square centimeters

Total surface area = 40 + 60 + 120 = 220 square centimeters

Therefore, the surface area of the triangular prism is 220 square centimeters.