Question

What is the surface area of the box shown by the pattern below?

Answer 1

Given the figure below:

The above figure, when closed, results into a cuboid.

This can be proven in the diagram below:

where the cuboid has

`\begin{gathered} \text{length}=7\text{ units} \\ \text{width}=5\text{ units} \\ \text{height}=2\text{ units} \end{gathered}`

The surface area of a cuboid is expressed as

`\begin{gathered} \text{Area = 2(L}* W)+2(L* H)+2(H* W) \\ \text{where} \\ L\Rightarrow\text{length} \\ W\Rightarrow\text{width} \\ H\Rightarrow\text{height} \end{gathered}`

Thus, the surface area of the cuboid is evaluated as

`\begin{gathered} \text{Area = 2(L}* W)+2(L* H)+2(H* W) \\ =2(7\text{ units}*5\text{ units)+2(7 units}*2\text{ units)+2(2 units}*5\text{ units)} \\ =2(35\text{ square units)+2(14 square units})+2(10\text{ square units)} \\ =(70+28+20)\text{ square units} \\ =118\text{ square units} \end{gathered}`

Hence, the surface area of the box is

`118\text{ square units}`

The correct option is D.