Answer:
[tex] 544 \, \textsf{cm}^2 [/tex]
Step-by-step explanation:
To find the surface area of the rectangular prism represented by the net, we need to sum the areas of all its faces.
Given:
Length of the prism, [tex] \textsf{length} = 16 [/tex] cm
Width of the prism, [tex] \textsf{width} = 8 [/tex] cm
Height of the prism, [tex] \textsf{height} = 6 [/tex] cm
The rectangular prism (Area = length × width) has 6 faces:
Top face:
[tex] 16 \times 8 [/tex] cm[tex]^2[/tex]
Bottom face:
[tex] 16 \times 8 [/tex] cm[tex]^2[/tex]
Front face:
[tex] 16 \times 6 [/tex] cm[tex]^2[/tex]
Back face:
[tex] 16 \times 6 [/tex] cm[tex]^2[/tex]
Left side face:
[tex] 8 \times 6 [/tex] cm[tex]^2[/tex]
Right side face:
[tex] 8 \times 6 [/tex] cm[tex]^2[/tex]
Now, we calculate the areas:
Top and bottom faces:
[tex] 2 \times (16 \times 8) = 2 \times 128 = 256 [/tex] cm[tex]^2[/tex]
Front and back faces:
[tex] 2 \times (16 \times 6) = 2 \times 96 = 192 [/tex] cm[tex]^2[/tex]
Left and right side faces:
[tex] 2 \times (8 \times 6) = 2 \times 48 = 96 [/tex] cm[tex]^2[/tex]
Total Surface Area:
[tex] \textsf{Total Surface Area} = \textsf{Top and bottom} + \textsf{Front and back} + \textsf{Left and right} [/tex]
[tex] = 256 + 192 + 96 [/tex]
[tex] = 544 \, \textsf{cm}^2 [/tex]
Therefore, the surface area of the rectangular prism represented by the net is:
[tex] 544 \, \textsf{cm}^2 [/tex]
Additional comment:
we can find surface areas using formulas too.
The surface area ([tex]SA[/tex]) of a rectangular prism can be calculated using the formula:
[tex] \Large\boxed{\boxed{SA = 2lw + 2lh + 2wh}} [/tex]
where:
- [tex] l [/tex] is the length of the rectangular prism,
- [tex] w [/tex] is the width of the rectangular prism, and
- [tex] h [/tex] is the height of the rectangular prism.
Given:
[tex] l = 16 \, \textsf{cm} [/tex]
[tex] w = 8 \, \textsf{cm} [/tex]
[tex] h = 6 \, \textsf{cm} [/tex]
Now, plug these values into the formula:
[tex] SA = 2 \times 16 \times 8 + 2 \times 16 \times 6 + 2 \times 8 \times 6 [/tex]
[tex] SA = 256 + 192 + 96 [/tex]
[tex] SA = 544 \, \textsf{cm}^2 [/tex]
Therefore, the surface area of the rectangular prism represented by the given net is [tex] 544 \, \textsf{cm}^2 [/tex].
