Solve for the surface area of the triangular prism.10cm 10cm 6cm 8cm and 10cm (1 point)Responses320 square centimeters320 square centimeters180 square centimeters180 square centimeters280 square centimeters280 square centimeters260 square centimeters
To find the surface area of a triangular prism, you need to calculate the area of all the individual faces and then add them together.
Given the dimensions:
- The base of the triangular prism is a triangle with sides of 10cm, 6cm, and 8cm.
- The height of the prism is 10 cm.
1. The area of the triangular base can be calculated using Heron's formula:
s = (10 + 6 + 8) / 2 = 12
Area = √(12 * (12 - 10) * (12 - 6) * (12 - 8))
Area = √(12 * 2 * 6 * 4)
Area = √(576)
Area ≈ 24 sq cm
2. The three lateral faces of the prism are rectangles. The area of the rectangles can be calculated as:
- 10 cm x 10 cm = 100 sq cm
- 10 cm x 6 cm = 60 sq cm
- 8 cm x 6 cm = 48 sq cm
3. Sum up the areas of all faces:
Total Surface Area = (2 * Area of the base) + (Sum of areas of lateral faces)
Total Surface Area = (2 * 24) + (100 + 60 + 48)
Total Surface Area = 48 + 208
Total Surface Area = 256 sq cm
Therefore, the surface area of the triangular prism is 256 square centimeters.
The closest answer provided is 260 square centimeters, which is the correct option.