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?
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.