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 perimeter \(P\) of the base

The base is a rectangle with length \(l = 8m\) and width \(w=4m\). The perimeter formula for a rectangle is \(P = 2(l + w)\).

$$P=2(8 + 4)=2\times12 = 24m$$

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

The height of the prism \(h = 6m\). Using the formula \(LA=hP\).

$$LA = 6\times24=144m^{2}$$

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

The area of the rectangular base \(B=l\times w\).

$$B = 8\times4=32m^{2}$$

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

Using the formula \(SA=LA + 2B\).

$$SA=144+2\times32$$

$$SA=144 + 64$$

$$SA=208m^{2}$$

Answer:

\(208\)