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
A. 142cm2 B. 132cm2 C. 122cm2 D. 112cm2
Correct Answer: 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