Jan is making a pencil holder out of plastic canvas.The pencil holder will be 4 inches high. It will not have a top.The perimeter of the square base is 17.64 inches.How much plastic canvas does Jan need?

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To determine how much plastic canvas Jan needs, we need to calculate the area of the base of the pencil holder.

Given:
- The pencil holder is in the shape of a square base.
- The perimeter of the base is 17.64 inches.
- The height of the pencil holder is 4 inches.

Step 1: Calculate the length of one side of the square base.
Perimeter = 4s, where s is the length of one side of the square base.
17.64 = 4s
Divide both sides by 4: s = 4.41 inches

Step 2: Calculate the area of the base.
Area of a square = side * side
Area = 4.41 * 4.41
Area = 19.48 square inches

Since Jan is making a pencil holder without a top, the plastic canvas should only cover the sides of the pencil holder.

Step 3: Calculate the surface area of the sides.
The surface area of a rectangular prism (the pencil holder without a top) is given by 2 * length * height + 2 * width * height.

Since we have a square base, the length and width are the same as the side length calculated earlier.

Surface area = 2 * s * h + 2 * s * h
Surface area = 2 * 4.41 * 4 + 2 * 4.41 * 4
Surface area = 70.56 square inches

Therefore, Jan needs 70.56 square inches of plastic canvas to make the pencil holder.