The cross section section of a uniform prism is a right-angled triangle with sides 3cm….

The cross section section of a uniform prism is a right-angled triangle with sides 3cm. 4cm and 5cm. If its length is 10cm. Calculate the total surface area

Correct Answer: Option B

Explanation

A prism has 3 rectangular faces and 2 triangular faces and 2 rectangular faces = 10(3 + 4 + 5) = 120
Area of triangular faces = (sqrt{s(s – a) (s – b) (s – c)})
where s = (frac{a + b + c}{2})
= (frac{3 + 4 + 5}{2})
= (frac{12}{2})
= 6
Area of (bigtriangleup) = (sqrt{6(6 – 30(6 – 4)(6 – 5)})
= (sqrt{6 times 3 times 2 times 1}) = 6
Area of triangle faces = 2 x 6 = 12cm²
Total surface area = Area of rectangular face + Area of (bigtriangleup) = 120 + 12
= 132cm²