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The cross section section of a uniform prism is a right-angl...

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

View answer & explanation

Correct answer is B

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

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