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Question

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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Solution

The perimeter P of the prism is P=4×side, therefore, the perimeter of prism with side 2.5 cm is P=4×2.5=10 cm.

The general formula for the lateral surface area of a right prism is LSA=Ph where P represents the perimeter of the base and h represents the height of the prism.

Since the perimeter of the prism is P=10 cm and the height is h=6.5 cm, therefore, the lateral surface area is:

LSA=P×h=10×6.5=65 cm2
The general formula for the total surface area of a right prism is TSA=Ph+2B where P represents the perimeter of the base, h is the height of the prism and B is the area of the base.

Since LSA=Ph=65 cm2 and the base is B=2.5 cm, therefore, the total surface area is:

TSA=2(2.5)2+65=12.5+65=77.5cm2

Hence, lateral surface area is 65cm2 and total surface area is 77.5cm2.

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