Question

A shoe box is 10 inches long and 6 inches wide. It is 3 inches tall.

Sage is wrapping the shoe box and determined that she needs 20% more than the total surface area in gift wrap to cover the box and account for overlap.


Sage needs ______ square inches of gift.


(Round answer to nearest tenth)

Answer 1

Sage needs 259.2 square inches of gift.

Explanation:

In order to solve this problem we need to calculate the surface area of the shoe box, which has a shape of a rectangular prism. A rectangular prism has three types of surfaces that are mirrored, the first one is formed by the length and width, the second one is formed by the length and height and the third one is formed by the width and height. We need to calculate the area of each of these surfaces and multiply by two. We have:

surface area = 2*width*height + 2*length*height + 2*width*length

surface area = 2*6*3 + 2*10*3 + 2*6*10 = 36 + 60 + 120 = 216 square inches

Since we need 20% more paper we need to multiply the area by 1,2. We have:

paper = 1.2*(surface area) = 1.2*216 = 259.2 square inches

Answer 2

Answer: 259.2

Explanation:

Hi, since the shoe box is a rectangular prism we have to apply the next formula to calculate the surface area if the box:

Surface area (A) = 2wl + 2lh + 2hw

Where:

w = width

l = length

h = height

Replacing with the vales given:

A = 2 (6x 10)+ 2 ( 10x3)+ 2 (3x 6)

A = 2 (60) + 2 (30) + 2(18)

A = 120+ 60+36

A =216 inches

Since she needs 20% more than the total surface area in gift wrap, we have to multiply the total surface area by the 20_% in decimal form, and then add that value to the total surface area.

216 x (20/100) = 43.2

Adding that value to the total surface area:

216 + 43.2 = 259.2 square inches