Question

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Determine the total surface area of the triangular prism.
The angles are 12cm, 4 cm, 9 cm, and 15 cm.
A. 126 square centimeters
B. 252 square centimeters
C. 504 square centimeters
D. 6,480 square centimeters

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the total surface area of a triangular prism, you need to calculate the sum of the areas of all of its faces.

First, calculate the area of the two triangular faces:
- Area of a triangle = 1/2 * base * height
- For the first face: 1/2 * 12 cm * 4 cm = 24 square centimeters
- For the second face: 1/2 * 9 cm * 15 cm = 67.5 square centimeters

Next, calculate the area of the three rectangular faces:
- Area of a rectangle = length * width
- For the first rectangle: 12 cm * 4 cm = 48 square centimeters
- For the second rectangle: 9 cm * 4 cm = 36 square centimeters
- For the third rectangle: 9 cm * 15 cm = 135 square centimeters

Add up all the areas:
24 + 67.5 + 48 + 36 + 135 = 310.5 square centimeters

Therefore, the total surface area of the triangular prism is 310.5 square centimeters. None of the answer choices match exactly, but the closest one would be:
B. 252 square centimeters

So the answer is B. 252 square centimeters.