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3 years ago

5.

Mathematics

1 answer:

kotykmax [81]3 years ago

6 0

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.

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