Question

find the surface area of this prism.
surface area of a prism
la = hp
sa = la + 2b
sa = ? cm²

Explanation:

Step1: Calculate the perimeter \(P\) of the base

The base is a rectangle with length \(l = 8\) cm and width \(w=2\) cm. The perimeter formula for a rectangle is \(P = 2(l + w)\).
\(P=2(8 + 2)=2\times10 = 20\) cm.

Step2: Calculate the lateral - surface area \(LA\)

The height \(h\) of the prism (the distance between the two bases) is \(h = 4\) cm. Using the formula \(LA=hP\).
\(LA = 4\times20=80\) \(cm^{2}\).

Step3: Calculate the area of the base \(B\)

The area formula for a rectangle (base) is \(B=l\times w\).
\(B = 8\times2=16\) \(cm^{2}\).

Step4: Calculate the total surface area \(SA\)

Using the formula \(SA=LA + 2B\).
\(SA=80+2\times16\).
First, calculate \(2\times16 = 32\). Then \(SA=80 + 32\).

Answer:

\(112\)