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.
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 answer