Question

find the surface area of this prism. surface area of a prism $la = hp$ $sa = la + 2b$ $sa = square? m^{2}$

Explanation:

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

The base is a rectangle with length \(l = 5m\) and width \(w=2m\). The perimeter of a rectangle \(P = 2(l + w)\).

$$P=2(5 + 2)=2\times7 = 14m$$

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

The height of the prism \(h = 7m\). Using the formula \(LA=hP\).

$$LA = 7\times14=98m^{2}$$

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

The area of the rectangular base \(B=l\times w\), where \(l = 5m\) and \(w = 2m\).

$$B=5\times2 = 10m^{2}$$

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

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

$$SA=98+2\times10=98 + 20=118m^{2}$$

Answer:

\(118\)