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Gift Wrapping A gift box has the shape of a rectangular prism. How much wrapping
paper do you need to cover the box?
You need
in.2 of paper to cover the box.
C
16 in
12 in

Gift Wrapping A gift box has the shape of a rectangular prism How much wrapping paper do you need to cover the box You need in2 of paper to cover the box C 16 i class=

Respuesta :

SumitRoy07

To calculate the amount of wrapping paper needed to cover the gift box, we need to find the surface area of the box.

A rectangular prism has six faces, and each face is a rectangle. The surface area of a rectangular prism can be found by adding the areas of all six faces.

Given:

Length (L) = 16 inches

Width (W) = 12 inches

Height (H) = 4 inches

The six faces of the rectangular prism are:

1. Top face: Length (L) × Width (W)

2. Bottom face: Length (L) × Width (W)

3. Front face: Length (L) × Height (H)

4. Back face: Length (L) × Height (H)

5. Left face: Width (W) × Height (H)

6. Right face: Width (W) × Height (H)

Calculating the surface area of the box:

Surface Area = 2 × (Length × Width) + 2 × (Length × Height) + 2 × (Width × Height)

= 2 × (16 × 12) + 2 × (16 × 4) + 2 × (12 × 4)

= 2 × (192) + 2 × (64) + 2 × (48)

= 384 + 128 + 96

= 608 in²

Therefore, to cover the gift box, you would need 608 square inches of wrapping paper.[tex][/tex]

Intriguing456

Answer:

608 in²

Step-by-step explanation:

To figure out how much wrapping paper we need to cover the box, we can find its surface area.

The surface area of a rectangular prism (a box) is defined as:

[tex]SA = 2A + (P \cdot d)[/tex]

where [tex]A[/tex] is the area of the base, [tex]P[/tex] is the perimeter of the base, and [tex]d[/tex] is the prism's depth.

From the diagram, we can identify the following values for these variables:

[tex]A=16\cdot 12 = 192 \text{ in}^2[/tex]

[tex]P = 16 + 12 + 16 + 12 = 56 \text{ in}[/tex]

[tex]d = 4\text{ in}[/tex]

Now, we can plug these values in for the variables in the above formula and solve for the prism's surface area.

[tex]SA = 2A + (P \cdot d)[/tex]

[tex]SA = 2(192) + (56 \cdot 4)[/tex]

[tex]SA = 384 + 224[/tex]

[tex]SA = 608 \text{ in}^2[/tex]

So, we need 608 in² of paper to cover the box.

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