Answer:
Part A
The total surface area of the triangular prism is approximately 1715.793 cm³
Part B
The volume of the triangular prism is 1,476 cm³
Step-by-step explanation:
Part A
The given parameters are;
The shape of the cross-section of triangular prism = Right-angled isosceles triangle
The length of one the of the equal side = 6 cm
The length of the prism = 82 cm
Therefore, the height of the triangular cross section of the prism = 6 × sin(45°) = 3·√2 cm
The base length of the cross section, l = √(6² + 6²) = √72 = 6·√2 cm
The area of the triangular cross section of the triangular prism = 1/2 × Base × Height
∴ The area of the triangular cross section of the triangular prism = 1/2 × 6·√2 cm × 3·√2 cm = 18 cm²
The total surface area of the triangular prism = 6 × 82 × 2 + 82 × 6×√2 + 2 × 18 ≈ 1715.793 cm³
The total surface area of the triangular prism ≈ 1715.793 cm³
Part B
The volume of the triangular prism = The area of the triangular cross section × The length of the triangular prism
∴ The volume of the triangular prism = 18 cm² × 82 cm = 1,476 cm³.
