Question

follow the steps to find the surface area of the square prism. what is the area of the top and bottom? top and bottom:? front and back: sides: total sa: 3 cm 8 cm 3 cm

Explanation:

Step1: Find area of top - bottom

The top and bottom are squares with side length $a = 3$ cm. The area of a square is $A=a^2$. So the area of one square is $A_1 = 3\times3=9$ $cm^2$. The combined area of top and bottom is $A_{tb}=2\times9 = 18$ $cm^2$.

Step2: Find area of front - back

The front and back are rectangles with length $l = 8$ cm and width $w = 3$ cm. The area of a rectangle is $A = l\times w$. So the area of one rectangle (front or back) is $A_2=8\times3 = 24$ $cm^2$. The combined area of front and back is $A_{fb}=2\times24=48$ $cm^2$.

Step3: Find area of sides

The sides are rectangles with length $l = 8$ cm and width $w = 3$ cm. The area of one side - rectangle is $A_3=8\times3 = 24$ $cm^2$. The combined area of the two sides is $A_{s}=2\times24 = 48$ $cm^2$.

Step4: Find total surface area

The total surface area $SA=A_{tb}+A_{fb}+A_{s}$. Substituting the values we found: $SA=18 + 48+48=114$ $cm^2$.

Answer:

Top and bottom: $18$ $cm^2$
Front and back: $48$ $cm^2$
Sides: $48$ $cm^2$
Total SA: $114$ $cm^2$