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. Front triangular face: Area = 0.5 * base * height = 0.5 * 5 * 11 = 27.5 square centimeters
2. Back triangular face (hidden): Since it is the same as the front triangular face, the area is also 27.5 square centimeters.
3. Right rectangular face: Area = length * width = 11 * 5 = 55 square centimeters
4. Left rectangular face (hidden): Since it is the same as the right rectangular face, the area is also 55 square centimeters.
5. Top rectangular face: This face is formed by the hypotenuse of the front and back triangles. We know that the hypotenuse (width of the visible rectangular face) is 5 centimeters. Using the Pythagorean theorem, we can calculate the height of the triangular face: sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5 centimeters. Therefore, the area of the top rectangular face is 5 * 11 = 55 square centimeters.
6. Bottom rectangular face (hidden): Since it is the same as the top rectangular face, the area is also 55 square centimeters.
Now, add all the areas together:
27.5 + 27.5 + 55 + 55 + 55 + 55 = 275 square centimeters
Therefore, the surface area of the triangular prism is 275 square centimeters.