1) 88.0 units^2
2) 60.0 units^2
3) 148.0 units^2
Explanation:
1)
The lateral area of a rectangular prism is equal to the sum of the areas of the 4 lateral faces.
Since the areas of 2 opposite faces are equal, the lateral area is:
[tex]A_L=2A_1 + 2A_2[/tex]
where [tex]A_1,A_2,A_3[/tex] are the areas of the two faces.
Here we have:
L = 6 is the length of the base
w = 5 is the width of the base
h = 4 is the height of the prism
So we have:
[tex]A_1=L\cdot h = (6)(4)=24[/tex]
[tex]A_2=w\cdot h =(5)(4)=20[/tex]
So the lateral surface area is
[tex]A_L = 2(24)+2(20)=88[/tex]
2)
The area of one base of the prism is the product of the length of the base and the width:
[tex]A=L\cdot w[/tex]
Where here we have
L = 6 is the length of the base
w = 5 is the width of the base
So the area of 1 base is
[tex]A=(6)(5)=30[/tex]
And here we have 2 bases, therefore the area of the two bases together is twice the area of the single base:
[tex]A_b=2A=2(30)=60[/tex]
3)
The total surface area of the prism is given by the sum of the area of the two bases + the lateral area of the prism:
[tex]A=A_b+A_L[/tex]
where
[tex]A_b[/tex] is the area of the bases
[tex]A_L[/tex] is the lateral area
Here for this prism we have:
[tex]A_b=60[/tex] (area of the bases)
[tex]A_L=88[/tex] (lateral area)
So the total surface area is
[tex]A=60+88=148[/tex]
Answer:
88 units squared
60 units squared
148 units squared
