Question

find the surface area of this prism. 6 m 8 m 4 m surface area of a prism la = hp sa = la + 2b sa = ? m²

Explanation:

Step1: Calculate the lateral area (LA)

The formula for the lateral area of a prism is \(LA = hP\), where \(h\) is the height of the prism and \(P\) is the perimeter of the base.
The base is a rectangle with length \(l = 8m\) and width \(w=4m\). The perimeter of the base \(P=2(l + w)=2(8 + 4)=2\times12 = 24m\). The height \(h = 6m\).
So, \(LA=hP=6\times24 = 144m^{2}\)

Step2: Calculate the area of the base (S)

The area of the base \(S=l\times w\), where \(l = 8m\) and \(w = 4m\). So, \(S=8\times4=32m^{2}\)

Step3: Calculate the surface area (SA)

The formula for the surface area of a prism is \(SA=LA + 2S\).
We know \(LA = 144m^{2}\) and \(S = 32m^{2}\). Then \(SA=144+2\times32\)
\(SA=144 + 64\)
\(SA=208m^{2}\)

Answer:

\(208\)