Question

Question 3 (1 point)Using the Rectangular Prism in the picture, find the Lateral Area, the Area of a Single Base, and the TOTAL Surface Area:3 in6 in8 inUse the face with dimensions 8in x 6in as the base.Lateral Area =in²Single Base Area =in²Surface Area =Blank 1:Blank 2:Blank 3:in²

Answer 1

To calculate the surface area, we will use the formula below

The lateral surface area of a cuboid is the value of the surface area of a cuboid excluding its top and bottom surfaces. The formula for the lateral surface area of a cuboid is expressed as,

`\begin{gathered} L.A=2h(l+w) \\ h=3in \\ l=8in \\ w=6in \end{gathered}`

By substituting the values, we will have

`\begin{gathered} L.A=2h(l+w) \\ L.A=2(3)(8+6) \\ L.A=6(14)in^2 \\ L.A=84in^2 \end{gathered}`

Hence,

The lateral area is

`\Rightarrow84in^2`

Part B:

Since the shape of the cuboid is a rectangle, to figure out the area of the single base, we will

use the formula below

`\begin{gathered} Area\text{ }of\text{ }single\text{ }base=l* b \\ l=8in,b=6in \end{gathered}`

By substituting the values, we will have

`\begin{gathered} Areaofsinglebase=l* b \\ Areaofsinglebase=8in*6in \\ Areaofsinglebase=48in^2 \end{gathered}`

Hence,

The area of the single base is

`\Rightarrow48in^2`

Part C:

To figure out the total surface area of the cuboid, we will use the formula below

`\begin{gathered} S.A=2(lw+lh+wh) \\ S.A=2(8*6)+(8*3)+(6*3) \\ S.A=2(48+24+18) \\ S.A=2(90) \\ S.A=180in^2 \\ \\ Alternatively, \\ S.A=lateral\text{ }area+2(area\text{ }of\text{ }base) \\ S.A=84in^2+2(48in^2) \\ S.A=84in^2+96in^2 \\ S.A=180in^2 \end{gathered}`

Hence,

The total surface area is

`\Rightarrow180in^2`