A triangular prism has a base formed by a triangle
A triangular prism has a base formed by a triangle with side lengths 9 cm, 12 cm, and 15 cm, If the height of the prism (Perpendicular to the base) is 10 cm, calculate its lateral surface area.
एक त्रिभुजाकार प्रिज्म का आधार 9 सेमी, 12 सेमी और 15 सेमी भुजाओं वाले त्रिभुज से बना है। यदि प्रिज्म की ऊँचाई (आधार पर लंबवत) 10 सेमी है, तो उसका पार्श्व पृष्ठीय क्षेत्रफल ज्ञात कीजिए।
Detailed Solution & Logic
Correct Answer:
\(360 \text{cm}^2\)
Solution:
The base of the prism is a triangle with sides 9 cm, 12 cm, and 15 cm.
This is a right-angled triangle because $9^2 + 12^2 = 15^2$.
So, its sides act as the perimeter for lateral surface area.
Lateral surface area of a prism
= Perimeter of base × height
Perimeter of triangle
$= 9 + 12 + 15 = 36$ cm
Height of prism = 10 cm
Lateral surface area
$= 36 \times 10 = 360$ cm²
Answer: The lateral surface area is $360 \text{ cm}^2$.
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