The figure shown can be folded along the lines to form a rectangular prism. The surface area of the rectangular prism, in $\mathrm{cm}^{2}$, is
(A) 312
(B) 300
(D) 84
(E) 600
(C) 280

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-090.jpg?height=268&width=491&top_left_y=1178&top_left_x=1229)
The figure shown can be folded along the lines to form a rectangular prism. The surface area of the rectangular prism, in $\mathrm{cm}^{2}$, is
(A) 312
(B) 300
(C) 280
(D) 84
(E) 600

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-388.jpg?height=317&width=596&top_left_y=264&top_left_x=1255)

## Solution

The required surface area is $2(5 ¥ 6+5 ¥ 10+6 ¥ 10)=280 \mathrm{~cm}^{2}$. Alternatively, if we fold the net into a rectangular box, we would obtain the following diagram. From this we can see that the faces of the box are two rectangles of area $30 \mathrm{~cm}^{2}$, two rectangles of area $50 \mathrm{~cm}^{2}$, and two rectangles of area $60 \mathrm{~cm}^{2}$. This gives a total surface area of $280 \mathrm{~cm}^{2}$.

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-388.jpg?height=282&width=331&top_left_y=694&top_left_x=1385)

ANswer: (C)