Question

Nadia plans to paint her jewelry box. The box is shaped like a rectangular prism with the dimensions

shown. which is closest to the total surface area of the jewelry box?
​

Answer 1

`132\ in^(2)` is closest to the total surface area of the box

Explanation:

we know that

The surface area of the box is equal to

`SA=2B+PH`

where

B is the area of the base

P is the perimeter of the base

H is the height of the box

we have

`L=7(3)/(4)\ in=(7*4+3)/(4)=(31)/(4)\ in`

`W=3(1)/(4)\ in=(3*4+1)/(4)=(13)/(4)\ in`

`H=3(7)/(8)\ in=(3*8+7)/(8)=(31)/(8)\ in`

Find the area of the base B

`B=LW`

`B=((31)/(4))((13)/(4))=(403)/(16)\ in^(2)`

Find the perimeter of the base P

`P=2(L+W)`

`P=2((31)/(4)+(13)/(4)))`

`P=2((44)/(4))=22\ in`

Find the surface area

`SA=2((403)/(16))+22((31)/(8))`

`SA=((403)/(8))+((682)/(8))`

`SA=(1,085)/(8)=135.625\ in^(2)`