Question

find the surface area of
the rectangular prism.
first, find the area of the
base and top rectangles.
area of the base
and top: ? cm²
area of the side
rectangles: cm²
area of the front
and back: cm²
total area: cm²
(the diagram shows a rectangular prism with length 6 cm, width 12 cm, height 2 cm, and also a net of the prism.)

Explanation:

Step1: Calculate area of base and top

The base and top are rectangles with length \(12\) cm and width \(6\) cm. Area of a rectangle is \(A = lw\).
For base and top (2 rectangles): \(A_{1}=2\times(12\times6)= 144\) \(cm^{2}\)

Step2: Calculate area of side rectangles

The side rectangles have length \(12\) cm and width \(2\) cm. For two side rectangles: \(A_{2}=2\times(12\times2)=48\) \(cm^{2}\)

Step3: Calculate area of front and back

The front and back are rectangles with length \(6\) cm and width \(2\) cm. For front and back (2 rectangles): \(A_{3}=2\times(6\times 2)=24\) \(cm^{2}\)

Step4: Calculate total surface area

Total surface area \(A = A_{1}+A_{2}+A_{3}\)
\(A=144 + 48+24=216\) \(cm^{2}\)

Answer:

Area of the base and top: \(144\) \(cm^{2}\)
Area of the side rectangles: \(48\) \(cm^{2}\)
Area of the front and back: \(24\) \(cm^{2}\)
Total Area: \(216\) \(cm^{2}\)