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:
![A_L=2A_1 + 2A_2](https://tex.z-dn.net/?f=A_L%3D2A_1%20%2B%202A_2)
where
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:
![A_1=L\cdot h = (6)(4)=24](https://tex.z-dn.net/?f=A_1%3DL%5Ccdot%20h%20%3D%20%286%29%284%29%3D24)
![A_2=w\cdot h =(5)(4)=20](https://tex.z-dn.net/?f=A_2%3Dw%5Ccdot%20h%20%3D%285%29%284%29%3D20)
So the lateral surface area is
![A_L = 2(24)+2(20)=88](https://tex.z-dn.net/?f=A_L%20%3D%202%2824%29%2B2%2820%29%3D88)
2)
The area of one base of the prism is the product of the length of the base and the width:
![A=L\cdot w](https://tex.z-dn.net/?f=A%3DL%5Ccdot%20w)
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
![A=(6)(5)=30](https://tex.z-dn.net/?f=A%3D%286%29%285%29%3D30)
And here we have 2 bases, therefore the area of the two bases together is twice the area of the single base:
![A_b=2A=2(30)=60](https://tex.z-dn.net/?f=A_b%3D2A%3D2%2830%29%3D60)
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:
![A=A_b+A_L](https://tex.z-dn.net/?f=A%3DA_b%2BA_L)
where
is the area of the bases
is the lateral area
Here for this prism we have:
(area of the bases)
(lateral area)
So the total surface area is
![A=60+88=148](https://tex.z-dn.net/?f=A%3D60%2B88%3D148)