5. The cross-section of a triangular prism is a right-angled isosceles triangle with one of the
equal side 6cm. If the length of the prism is 82 cm, calculate the total surface area and
volume of the prism.
which is wailable from your science practical
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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.