Question : The base of a right prism is an equilateral triangle whose side is 10 cm. If the height of this prism is $10 \sqrt{3}$ cm, then what is the total surface area of the prism?
Option 1: $125 \sqrt{3}$ cm2
Option 2: $325 \sqrt{3}$ cm2
Option 3: $150 \sqrt{3}$ cm2
Option 4: $350 \sqrt{3}$ cm2
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Correct Answer: $350 \sqrt{3}$ cm 2
Solution :
Given: The base of a right prism is an equilateral triangle whose side is 10 cm.
The height of this prism is $10 \sqrt{3}$ cm.
The total surface area of the prism = [2(area of triangular base)] + [3(Area of rectangular sides)]
The area of an equilateral triangle = $\frac{\sqrt3}{4}\times{\text{side}^2}$
The area of a rectangle = length × breadth
The area of an equilateral triangle $=\frac{\sqrt3}{4}\times{{10}^2}=25\sqrt3$ cm
2
The area of a rectangle $=10\times 10\sqrt3=100\sqrt3 $ cm
2
The total surface area of the prism $=2\times 25\sqrt3+3\times 100\sqrt3$
$=50\sqrt3+300\sqrt3=350 \sqrt{3}$ cm
2
Hence, the correct answer is $350 \sqrt{3}$ cm
2
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