The side of a square-based prism is 2.5cm and its height is 6.5cm. Find its lateral and total surface area.

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lateral surface area = 33.05 𝑐𝑚2 and Total Surface Area = 39.29 𝑐𝑚2

lateral surface area = 55.05 𝑐𝑚2 and Total Surface Area = 19.22 𝑐𝑚2

lateral surface area = 44.03 𝑐𝑚2 and Total Surface Area = 33.22 𝑐𝑚2

lateral surface area = 11.09 𝑐𝑚2 and Total Surface Area = 22.99 𝑐𝑚2

answer is A.

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Detailed Solution

Firstly to slant height of the prism and the value of that height,
6.52 +

( 2.5)2
2

⇒ √42.25 + 1.56
⇒ 6.61 cm
With the above value of the slant height and base of the triangle we get the area of each triangle ⇒
6.61 × 2.5 = 8.25 𝑐𝑚2
2
lateral surface area ⇒ 4 × 8.25 𝑐𝑚2 = 33.05 𝑐𝑚2
Area of the base of the prism ⇒ 2.5cm × 2.5cm = 6.25 𝑐𝑚2
∴ Total Surface Area = Area of the base of the prism + 4 × Area of the face of a triangle.
⇒ 6.25 𝑐𝑚2 + 4 × 8.25 𝑐𝑚2
⇒ 39.29 𝑐𝑚2
Thus, lateral surface area = 33.05 𝑐𝑚2 and Total Surface Area = 39.29 𝑐𝑚2.

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