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Question

Caleb bought a jewelry box. He wants to paint all of the exterior faces of the jewelry box. How much paint does he need?

Solve on paper, then enter your answer on Zearn. You can use the calculator to help you solve.

Caleb

's jewelry box

Caleb needs 

 square feet of paint

Answer 1

This is a surface area question. In order to solve this, you have to figure out the total surface area of the shape, and that will tell you how much paint he needs. We can literally find the "surface area": i.e., the area of each surface individually, just by using the formula for the area of a rectangle: A=L*W, area = length times width.

To make your life a little easier, there is a total of 8 faces to calculate the area of, and 6 of them are rectangles, so you can use that formula directly and add them all up. There are 2 faces that are not rectangles, but it is also possible to break those up in your head into two rectangles of different shapes by making an imaginary cut along one straight line.

In total, if you do this, you should have 10 total A=L*W calculations (8 if you're efficient). Now comes the harder part, figuring out all the L's and W's. You can do this by adding and subtracting other numbers you know. I'll give you an example: we don't know the length of the edge directly next to the "7ft" edge, but we know that the opposite side is 10ft long, and the other edge close to is is 4ft long. Subtracting these, this new edge must be 6ft. Use your spatial reasoning like this to write all of the edge lengths on the shape first, and then do the area calculation.

Hope this helps!