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AVprozaik [17]
3 years ago
11

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

Mathematics
1 answer:
Pachacha [2.7K]3 years ago
6 0

Answer:

132\ in^{2} is closest to the total surface area of the box

Step-by-step 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\frac{3}{4}\ in=\frac{7*4+3}{4}=\frac{31}{4}\ in

W=3\frac{1}{4}\ in=\frac{3*4+1}{4}=\frac{13}{4}\ in

H=3\frac{7}{8}\ in=\frac{3*8+7}{8}=\frac{31}{8}\ in

<em>Find the area of the base B</em>

B=LW

B=(\frac{31}{4})(\frac{13}{4})=\frac{403}{16}\ in^{2}

<em>Find the perimeter of the base P</em>

P=2(L+W)

P=2(\frac{31}{4}+\frac{13}{4}))

P=2(\frac{44}{4})=22\ in

<em>Find the surface area</em>

SA=2(\frac{403}{16})+22(\frac{31}{8})

SA=(\frac{403}{8})+(\frac{682}{8})

SA=\frac{1,085}{8}=135.625\ in^{2}

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