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 find the area of each individual face and then add them together.
1. The area of the front triangular face can be calculated using the formula for the area of a triangle: A = 1/2 * base * height. In this case, the base is 5 cm and the height is 4 cm.
Area of the triangular face = 1/2 * 5 cm * 4 cm = 10 square cm.
2. The area of the right rectangular face is simply the length times the width, which is 11 cm * 5 cm = 55 square cm.
3. The other three faces of the triangular prism are identical to the right rectangular face, so the area of each of these faces is also 55 square cm.
Adding up all the areas:
Total surface area = 10 square cm + 55 square cm + 55 square cm + 55 square cm = 175 square cm.
Therefore, the surface area of the triangular prism is 175 square centimeters.