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Jessica is wrapping a gift in a rectangular box with gift wrapping paper for a birthday party. The box is 11 inches long, 8 inches wide, and 5 inches tall. How much gift-wrapping paper will she need to wrap the box?

Question:

A
366 in².

explanation

Step 1: Interpret the Problem

First, we must understand what is happening in this situation. We need to know how much gift wrapping paper Jessica needs to wrap the gift. Since the box, she is wrapping it in is a rectangular prism, we need to find the surface area of the box.

Step 2: Break Your Shape Down Into Its Net

When we break down a rectangular prism into its net, we have six rectangles, a top and a bottom, a front, and a back, and two sides.

Step 3: Determine How to Find the Area of Each Part of the Net

Let’s first find the area of the top and the bottom rectangles of the prism. Since these two shapes are exactly the same, we can find the area of one and then multiply it by two.

Here’s how we find the area of a rectangle.
*length × width = area*

The length of the top rectangle is 11 in and the width is 8 in.

We can plug it into the equation.

11 in × 8 in = 88 in2

The area of the top and bottom rectangles are 88 in2 each.

Now we find the area of the front and back rectangles.

Next let’s find the area of the front and back rectangles of the prism. Since these two shapes are exactly the same, we can find the area of one and then multiply it by two.

Here’s how we find the area of a rectangle.
*length × width = area*

The length of the front rectangle is 11 in and the width is 5 in.

We can plug it into the equation.

11 in × 5 in = 55 in2

The area of the front and back rectangles are 55 in2 each.

Lastly we find the area of the two side rectangles.

Finally let’s find the area of the 2 side rectangles of the prism. Since these two shapes are exactly the same, we can find the area of one and then multiply it by two.

Here’s how we find the area of a rectangle.
*length × width = area*

The length of a side rectangle is 8 in and the width is 5 in.

We can plug it into the equation.

8 in × 5 in = 40 in2

The area of each of the side rectangles is 40 in2.

Step 4: Add Up the Areas of Each Part of the Net

We have found the area of the top rectangle, front rectangle, and one side rectangle, so now we multiply their areas by two and add them to find the surface area of the rectangular prism.

2 × top area + 2 × bottom area + 2 × side area = surface area

Now let’s plug it in.

2 × 88 in2 + 2 × 55 in2 + 2 × 40 in2

Now we can solve for the surface area following the order of operations.

First – we multiply:

2 × 88 in2 + 2 × 55 in2 + 2 × 40 in2 = 176 in2 + 110 in2 + 80 in2

Now we add to solve by addition:

176 in2 + 110 in2 + 80 in2 = 366 in2

So, Jessica needs 366 in² of gift wrap paper.

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Comments

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3 years ago

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3 years ago

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3 years ago

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