Solve for the surface area of the triangular prism. 10cm, 10cm, 10cm, 8cm, 6cm (1 point) Responses
To find the surface area of a triangular prism, you need to calculate the area of the two triangular bases and the three rectangular faces.
The formula for the surface area of a triangular prism is:
Surface Area = 2*(base area of triangle) + (perimeter of triangle) * height
Given that the base of the triangle is 10cm, and the height is 8cm, the area of one triangle would be:
Area = (1/2) * base * height
Area = (1/2) * 10cm * 8cm
Area = 40cm²
Since there are two triangles in a prism, the total area of the triangular bases would be:
Total base area = 2 * 40cm²
Total base area = 80cm²
Now, calculate the perimeter of the triangle:
Perimeter = 10cm + 10cm + 10cm
Perimeter = 30cm
Now calculate the surface area of the three rectangular faces:
1. With dimensions 10cm x 8cm: 10cm * 8cm = 80cm²
2. With dimensions 10cm x 6cm: 10cm * 6cm = 60cm²
3. With dimensions 8cm x 6cm: 8cm * 6cm = 48cm²
Now, add the areas of the two triangular bases and the three rectangular faces to get the total surface area of the triangular prism:
Total Surface Area = 80cm² + 80cm² + 60cm² + 48cm²
Total Surface Area = 268cm²
Therefore, the surface area of the triangular prism is 268cm².