Answer:
880.16 in²
Step-by-step explanation:
To find out how much wrapping paper Tiana needs to buy, we need to calculate the total surface area of the two boxes.
Each box has six faces: top, bottom, front, back, left side, and right side.
The surface area of one box is given by the formula:
[tex] \textsf{Surface Area} = 2lw + 2lh + 2wh [/tex]
Where:
- [tex] l [/tex] is the length,
- [tex] w [/tex] is the width, and
- [tex] h [/tex] is the height of the box.
For the first box:
- [tex] l = 12.2 [/tex] inches,
- [tex] w = 5.2 [/tex] inches, and
- [tex] h = 9 [/tex] inches.
Let's calculate the surface area for one box:
[tex] \textsf{Surface Area}_{\textsf{box 1}} = 2(12.2 \times 5.2) + 2(12.2 \times 9) + 2(5.2 \times 9) [/tex]
[tex] \textsf{Surface Area}_{\textsf{box 1}} = 2(63.44) + 2(109.8) + 2(46.8) [/tex]
[tex] \textsf{Surface Area}_{\textsf{box 1}} = 126.88 + 219.6 + 93.6 [/tex]
[tex] \textsf{Surface Area}_{\textsf{box 1}} = 440.08 \textsf{ square inches} [/tex]
Now, since Ariel needs to wrap two gifts, the total surface area of wrapping paper needed is:
[tex] \textsf{Total Surface Area} = 2 \times \textsf{Surface Area}_{\textsf{box 1}} [/tex]
[tex] \textsf{Total Surface Area} = 2 \times 440.08 [/tex]
[tex] \textsf{Total Surface Area} = 880.16 \textsf{ square inches} [/tex]
Tiana needs to buy 880.16 in² of wrapping paper.
