What's the surface area of a triangular prism with a width of 6 cm a depth of 9 cm and a height of 8 cm in square centimeters
The surface area of a triangular prism is calculated by adding the areas of each of its faces.
In a triangular prism, there are 2 triangular faces and 3 rectangular faces. The formula to calculate the surface area of a triangular prism is:
Surface Area = 2(base area of triangle) + (perimeter of triangle × height of prism)
First, let's calculate the base area of the triangle:
Base area = 1/2 × base × height
Base area = 1/2 × 6 cm × 8 cm
Base area = 24 cm²
Next, let's calculate the perimeter of the triangle:
Perimeter = sum of all sides
Perimeter = 6 cm + 6 cm + 9 cm
Perimeter = 21 cm
Now, let's calculate the surface area of the triangular prism:
Surface Area = 2(24 cm²) + (21 cm × 8 cm)
Surface Area = 48 cm² + 168 cm²
Surface Area = 216 cm²
Therefore, the surface area of the triangular prism is 216 square centimeters.