Question

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

Answer 1

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.

Answer 2

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:

$SA = 2A + (P \cdot d)$

where $A$ is the area of the base, $P$ is the perimeter of the base, and $d$ is the prism's depth.

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

$A=16\cdot 12 = 192 \text{ in}^2$

$P = 16 + 12 + 16 + 12 = 56 \text{ in}$

$d = 4\text{ in}$

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

$SA = 2A + (P \cdot d)$

$SA = 2(192) + (56 \cdot 4)$

$SA = 384 + 224$

$SA = 608 \text{ in}^2$

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