Question

When Tyson opens a cereal box and lays it out flat, he sees that both the top and the bottom of the box measure 3 inches by 9 inches. Both sides of the box measures 3 inches by 12 inches, and both the front and back of the box measure 9 inches by 12. What is the surface area of the cereal box?

Answer 1

`A=342\ in^2`

Explanation:

Surface Areas

If some surface is made of smaller parts, the total area can be computed as the sum of the particular areas. The area of a rectangle of dimensions a and b is

`A=ab`

The cereal box is made of 6 rectangles. We'll calculate their areas and then add them to find the total area. For the top and the bottom, we compute twice the area of a rectangle

`A_1=2ab=2(3)(9)=54\ in^2`

The sides of the box measure 3 inches by 12 inches, their area is

`A_2=2(3)(12)=72\ in^2`

The front and back of the box measure 9 inches by 12

`A_3=2(9)(12)=216\ in^2`

The total area of the flattened cereal box is

`A=54+72+216=342\ in^2`

`\boxed{A=342\ in^2}`