a) Surface area: [tex]52 ft^2[/tex]
b) Volume: [tex]24 ft^3[/tex]
Step-by-step explanation:
a)
The surface area of the prism is the sum of the areas of all its faces.
The lengths of the sides of the prism are:
[tex]b=4 ft\\w=2 ft\\h = 3 ft[/tex]
where b, w and h are the base, width and height, respectively.
Therefore there are 2 faces (top and bottom) with area:
[tex]A_1 = bh =(4)(2)=8 ft^2[/tex]
Then there are 2 faces (left and right) with area:
[tex]A_2=wh=(2)(3)=6 ft^2[/tex]
And then, there are 2 faces (front and back) with area:
[tex]A_3=bh=(4)(3)=12 ft^2[/tex]
And so, the total surface area is
[tex]A=2A_1+2A_2+2A_3=2(8)+2(6)+2(12)=52 ft^2[/tex]
b)
The volume of a rectangular prism is given by
[tex]V=bwh[/tex]
where
b is the base
w is the width
h is the heigth
For the rectangular prism in this problem, we have:
b = 4 ft (base)
w = 2 ft (width)
h = 3 ft (height)
Therefore, the volume is
[tex]V=(4)(2)(3)=24 ft^3[/tex]
