Question

calculate the volume and the surface area

Explanation:

Step1: Calculate the volume

The formula for the volume \( V \) of a triangular prism is \( V=\frac{1}{2}bh\times l \), where \( b = 3\mathrm{cm} \), \( h = 4\mathrm{cm} \), and \( l=11\mathrm{cm} \).

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Step2: Calculate the surface area

The surface area \( S \) of a triangular prism is \( S = 2\times(\frac{1}{2}bh)+(b + h+5)\times l \).
First, find the area of the two triangular bases: \( 2\times(\frac{1}{2}\times3\times4)=12\mathrm{cm}^2 \).
Then, find the perimeter of the triangular base \( P=3 + 4+5 = 12\mathrm{cm} \), and the lateral surface area \( L = 12\times11=132\mathrm{cm}^2 \).

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Answer:

The volume is \( 66\mathrm{cm}^3 \) and the surface area is \( 144\mathrm{cm}^2 \).