To find the surface area of the triangular prism, we need to calculate the areas of each individual face and then sum them together.
1. Front triangular face:
Area = (1/2) * base * height
Area = (1/2) * 5 * 4
Area = 10 square centimeters
2. Back triangular face (same as front triangular face):
Area = 10 square centimeters
3. Right rectangular face:
Area = length * width
Area = 11 * 5
Area = 55 square centimeters
4. Left rectangular face (same as right rectangular face):
Area = 55 square centimeters
5. Top rectangular face:
This face is not visible, but we can calculate its area using the Pythagorean theorem to find the height:
Height = sqrt(4^2 + 3^2)
Height = 5 centimeters
Area = length * width
Area = 11 * 5
Area = 55 square centimeters
6. Bottom rectangular face (same as top rectangular face):
Area = 55 square centimeters
Now, summing all the areas together:
Surface Area = 10 + 10 + 55 + 55 + 55 + 55
Surface Area = 190 square centimeters
Therefore, the surface area of the triangular prism is 190 square centimeters.
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?
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