Use 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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To find the surface area of the triangular prism, we need to calculate the area of each individual face and then add them together.
1. Area of the front triangular face:
Area = 1/2 * base * height
Area = 1/2 * 5 * 12 (using Pythagorean theorem to find the height)
Area = 1/2 * 5 * 13
Area = 32.5 square centimeters
2. Area of the back triangular face (same as the front):
Area = 32.5 square centimeters
3. Area of the top rectangular face:
Area = length * width
Area = 5 * 11
Area = 55 square centimeters
4. Area of the bottom rectangular face (same as the top):
Area = 55 square centimeters
5. Area of the right rectangular face:
Area = width * height
Area = 11 * 12
Area = 132 square centimeters
6. Area of the left rectangular face (same as the right):
Area = 132 square centimeters
Now, add all the areas together to get the total surface area:
32.5 + 32.5 + 55 + 55 + 132 + 132 = 439 square centimeters
Therefore, the surface area of the triangular prism is 439 square centimeters.