Tiny space particles damaged the outside of the station's rectangular observation module. Nova, Luna, and Emek needed to cover all six surfaces with repair panels. The module measured 7 meters long, 5 meters wide, and 2 meters high. On its net, they identified two 7 by 5 faces, two 7 by 2 faces, and two 5 by 2 faces. Their areas were 35, 14, and 10 square meters. Luna doubled each area, and Emek added 70 + 28 + 20 to get 118 square meters. They prepared exactly 118 square meters of panels and repaired the module.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Find the area of each type of face, then remember that each type appears twice.
On the module's net, which pair of faces has a total area of 28 square meters?
The two 7 by 5 facesThe two 7 by 2 facesThe two 5 by 2 facesOne 7 by 5 face and one 5 by 2 faceCorrect! Each 7 by 2 face has an area of 14 square meters, so two have an area of 28 square meters.
Try again. Look for a face with an area of 14 square meters and account for both matching faces.
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Hint
Find the total area of the two 7 by 2 faces and the two 5 by 2 faces, then add those totals.
Suppose only the four side faces of the module need new panels. These are the two 7 by 2 faces and the two 5 by 2 faces. How many square meters of panels are needed?
Correct! The four side faces need 48 square meters of panels.
Try again. Add the areas of both 7 by 2 faces and both 5 by 2 faces.
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Hint
Think about why the net contains two faces of each size.
Nova suggests finding the module's total surface area with 2 * (7 * 5 + 7 * 2 + 5 * 2). Why does this method work?
It finds the volume first and then doubles it.It adds the lengths of all the edges and then doubles them.It finds one of each different face area and doubles the sum because each face has a matching opposite face.It finds the area of only the four side faces.Correct! Each of the three different face sizes appears twice, so their areas can be added and then doubled.
Try again. Connect each product inside the parentheses to one type of rectangular face on the net.
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