Question : If the altitude of a right prism is 10 cm and its base is an equilateral triangle of side 12 cm, then its total surface area (in cm2) is:
Option 1: $(5+3\sqrt3)$
Option 2: $36\sqrt3$
Option 3: $360$
Option 4: $72(5+\sqrt3)$
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Correct Answer: $72(5+\sqrt3)$
Solution :
Use the formulas:
Area of equilateral triangle of side $a =\frac{\sqrt3a^2}{4}$
The perimeter of an equilateral triangle of side $a = 3a$
Total surface area of prism = Perimeter of base × Height + 2 × Base area
Height of a right prism = 10 cm
Side of an equilateral triangle, $a$ = 12 cm
Base area $= \frac{\sqrt3a^2}{4} = \frac{\sqrt3}{4}×12×12 = 36\sqrt3$cm
2
Perimeter of base $= 3a = 3 × 12 = 36$ cm
Total surface area of prism = (Perimeter of base × Height + 2 × Base area)
$=36×10 + 2×36\sqrt3$
$= 360+72\sqrt3$
$= 72(5+\sqrt3)$ cm
2
Hence, the correct answer is $72(5+\sqrt3)$.
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