Question : The base of a prism is a right-angled triangle with two sides 5 cm and 12 cm. The height of the prism is 10 cm. The total surface area of the prism is:
Option 1: 360 sq cm
Option 2: 300 sq cm
Option 3: 330 sq cm
Option 4: 325 sq cm
Correct Answer: 360 sq cm
Solution :
Given: Height = 10 cm
Two sides = 5 cm and 12 cm
$\therefore$ Area of the base of the right prism = $\frac{1}{2}×5×12$ = 30 sq cm
Other side of the right-angled triangle $=\sqrt{5^2+12^2}=\sqrt{25+144} = 13$
Curved surface area = perimeter of base × height = (5 + 12 + 13) × 10 = 300 sq cm
$\therefore$ Total surface area = curved surface area + 2 (area of base) = 300 + 2 × 30 = 360 sq cm
Hence, the correct answer is 360 sq cm.
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