Ian is decorating the outside of a box in the shape of a right rectangular prism. The figure below shows a net for the box. What is the surface area of the box in square centimeters that Ian decorates?

Answer 1

To find the surface area of the box, we need to find the area of each of the six faces and then add them up.

Looking at the net, we can see that there are three pairs of faces that are congruent to each other (A and B, C and D, E and F).

The dimensions of the net are as follows:
- The dimensions of faces A and B: 5 cm x 10 cm
- The dimensions of faces C and D: 5 cm x 8 cm
- The dimensions of faces E and F: 10 cm x 8 cm

Now, let's calculate the area of each face:
- Area of face A: 5 cm x 10 cm = 50 sq cm
- Area of face B: 5 cm x 10 cm = 50 sq cm
- Area of face C: 5 cm x 8 cm = 40 sq cm
- Area of face D: 5 cm x 8 cm = 40 sq cm
- Area of face E: 10 cm x 8 cm = 80 sq cm
- Area of face F: 10 cm x 8 cm = 80 sq cm

Now, let's add up the areas of all the faces to get the total surface area of the box:
50 (A) + 50 (B) + 40 (C) + 40 (D) + 80 (E) + 80 (F) = 340 sq cm

Therefore, Ian decorates a total surface area of 340 square centimeters on the box.