Question

What is the surface area of the triangular prism

Answer 1

To calculate the surface area of a triangular prism, you first need to find the area of the two triangular bases and the three rectangular faces.

1. Calculate the area of the two triangular bases:
- A = 1/2 * base * height
- Given: base = 8 cm, height = 5 cm
- A = 1/2 * 8 cm * 5 cm = 20 cm^2 for one base
- Since there are two bases, the total area of the two bases = 2 * 20 cm^2 = 40 cm^2

2. Calculate the area of the three rectangular faces:
- The height of the prism = 10 cm
- The length of the rectangular faces is the same as the base of the triangle, which is 8 cm
- The width of the rectangular faces is the same as the height of the triangle, which is 5 cm
- There are three rectangular faces on a triangular prism, so the total area of the three rectangular faces = 2 * (height * length) + 2 * (height * width) + 2 * (length * width)
- Area = 2 * (10 cm * 8 cm) + 2 * (10 cm * 5 cm) + 2 * (8 cm * 5 cm) = 160 cm^2 + 100 cm^2 + 80 cm^2 = 340 cm^2

3. To find the total surface area, add the areas of the two triangular bases and the three rectangular faces:
Total surface area = 40 cm^2 + 340 cm^2 = 380 cm^2

Therefore, the surface area of the triangular prism is 380 cm^2.