The diagram shows a prism with a rectangular base, ABFE.
The cross-section, ABCD, is a trapezium with AD = BC.
AB = 8cm, GH = 5cm, BF = 12 cm and angle ABC = 70°.
(a) Calculate the total surface area of the prism.
Answers
Given : a prism with a rectangular base, ABFE.
The cross-section, ABCD, is a trapezium with AD = BC.
AB = 8cm, GH = 5cm, BF = 12 cm and angle ABC = 70°.
To Find : the total surface area of the prism.
Solution:
AB = 8 cm
DC = HG = 5 cm
DM ⊥ AB and CN⊥AB
MN = 5 cm
AD = BC
=> AM = BN = ( 8 - 5)/2 = 3/2 cm
tan 70° = CN / BN
=> tan 70° = CN /(3/2)
=> CN = 4.12 cm
Cos 70° = BN/BC
=> BC = 4.385 cm
Area of Trapezium = (1/2) (8 + 5) * 4.12 = 53.56/2
area of both Trapezium faces = 2 * 53.56/2 = 53.56 cm²
Area of remaining 4facse = Perimeter of trapezium * BF
= ( 8 + 4.385 + 5 + 4.385) 12
= 21.77 * 12
= 261.24 cm²
total surface area of the prism = 53.56 + 261.24 = 314.8 cm²
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