Question : The base of a right prism is a right-angled triangle whose sides are 5 cm, 12 cm, and 13 cm. If the area of the total surface of the prism is 360 cm2, then its height is:
Option 1: 10 cm
Option 2: 12 cm
Option 3: 9 cm
Option 4: 11 cm
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Correct Answer: 10 cm
Solution :
The area of the total surface of the prism = 360 cm
2
The base of the right-angled triangle = 5 cm
The perpendicular of the right-angled triangle = 12 cm
Hypotenuse of the right-angled triangle = 13 cm
Perimeter of base of prism = (5 + 12 + 13) = 30 cm
Base area = $\frac{1}{2}$ × base × perpendicular
= $\frac{1}{2}$ × 5 × 12
= 30 cm
2
Total surface area of prism = (Perimeter of base × Height + 2 × Base area)
⇒ 360 = 30 × height + 2 × 30
⇒ Height = $\frac{360 - 60}{30}$ = 10 cm
Hence, the correct answer is 10 cm.
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