The cross section section of a uniform prism is... - WAEC Mathematics 2011 Question
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 option: 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
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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