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 \(l = 5\) cm and width \(w=4\) cm. The perimeter formula for a rectangle is \(P = 2(l + w)\).

$$ P=2(5 + 4)=2\times9 = 18\text{ cm} $$

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

The height \(h\) of the prism (distance between the two bases) is \(h = 3\) cm. Using the formula \(LA=hP\).

$$ LA=3\times18=54\text{ cm}^2 $$

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

The area formula for a rectangle is \(B=l\times w\). Here, \(l = 5\) cm and \(w = 4\) cm.

$$ B=5\times4 = 20\text{ cm}^2 $$

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

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

$$ SA=54+2\times20=54 + 40=94\text{ cm}^2 $$

Answer:

\(94\)