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 face and then add them together.
1. The area of the front triangular face:
The area of a triangle can be calculated using the formula A = 1/2 * base * height.
In this case, the base is 5 cm and the height is 4 cm. So, the area of the front triangular face is:
A = 1/2 * 5 cm * 4 cm = 10 cm²
2. The area of the back triangular face:
Since the back triangular face is identical to the front triangular face, the area of the back triangular face is also 10 cm².
3. The area of the right rectangular face:
The area of a rectangle can be calculated by multiplying the width and length. In this case, the width is 5 cm and the length is 11 cm. So, the area of the right rectangular face is:
A = 5 cm * 11 cm = 55 cm²
4. The area of the top rectangular face:
Since the top rectangular face is identical to the right rectangular face, the area of the top rectangular face is also 55 cm².
5. The area of the bottom rectangular face:
The bottom rectangular face is the same size as the top and right rectangular faces, so the area of the bottom rectangular face is also 55 cm².
6. The total surface area of the triangular prism:
To find the total surface area of the triangular prism, we add up the areas of all the faces:
Total surface area = 10 cm² + 10 cm² + 55 cm² + 55 cm² + 55 cm² = 185 cm²
Therefore, the surface area of the triangular prism is 185 cm².