Question

Julian is decorating the outside of a box in the shape of a right rectangular prism. Thefigure below shows a net for the box.

Answer 1

The surface area of the box equals the sum of the surface area of each of its parts.

And the area of each rectangle that form the box is found by multiplying the width by the height of that rectangle.

We have two ractangles with sides 7 ft and 10 ft. So the area of each one is:

7 ft * 10 ft = 7 * 10 * ft * ft = 70 ft²

Since there's two of this rectangle, their areas sum up to

2 * 70 ft² = 140 ft²

Now, we also have two rectangles with sides 7 ft and 14 ft (the second and the fourth rectangles from left to right in the image). So, their areas sum up to:

2 * (7 ft * 14 ft) = 2 * (98 ft²) = 196 ft²

Finally, we also have two rectangles with sides 10 ft and 14 ft. Then, their area together is:

2 * (10 ft * 14 ft) = 2 * (140 ft²) = 280 ft²

Therefore the total surface area of the box is the sum:

140 ft² + 196 ft² + 280 ft² = 616 ft²