Question

find the volume and surface area of each of these prisms. (a) (b)

Explanation:

Step1: Calculate the volume of the prism

The volume \(V\) of a prism is given by \(V = A\times h\), where \(A\) is the area of the base and \(h\) is the height (length) of the prism.
The base is a triangle with base \(b = 10\mathrm{cm}\) and height \(h_{triangle}=12\mathrm{cm}\). The area of a triangle \(A=\frac{1}{2}\times b\times h_{triangle}\).

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The length of the prism \(l = 30\mathrm{cm}\). Then \(V=A\times l\)

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Step2: Calculate the surface area of the prism

The surface area \(S\) of a triangular - prism is \(S = 2A+ (a + b+ c)\times l\), where \(a = 13\mathrm{cm}\), \(b = 10\mathrm{cm}\), \(c = 13\mathrm{cm}\), \(A = 60\mathrm{cm}^{2}\) and \(l = 30\mathrm{cm}\)
First, \(2A=2\times60 = 120\mathrm{cm}^{2}\)
Second, \(a + b + c=13 + 10+13=36\mathrm{cm}\)
Then \((a + b + c)\times l=36\times30 = 1080\mathrm{cm}^{2}\)

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Answer:

The volume of the prism is \(1800\mathrm{cm}^{3}\) and the surface area is \(1200\mathrm{cm}^{2}\)