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The figure shows the dimensions for a package to be shipped.

A trapezoidal prism. The front and back are trapezoids.The distance from the trapezoidal front to the trapezoidal back is 15 inches.
The slant is on the right side. The Height on the left is 6 inches, On the top, the width from the left to the top of the slanted side is 4 inches. The distance of the slant from top to bottom is 10 inches. The entire width of the base from the left to right (that is, from the left side of 6 inches to the bottom of the slant) is 12 inches.



What is the minimum amount of wrapping paper, in square inches, needed to cover the package?

User Krackmoe
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1 Answer

7 votes

Answer:

Explanation:

To calculate the amount of wrapping paper needed to cover the package, we need to find the area of each face of the trapezoidal prism and add them together.

First, we can find the area of the trapezoidal front and back faces. The formula for the area of a trapezoid is:

Area = (a + b) / 2 * h

where a and b are the lengths of the parallel sides, and h is the height. For the front and back faces, we have:

Front/back area = ((6 + 12) / 2) * 15 = 135 square inches

Next, we can find the area of the top and bottom faces, which are rectangles. The formula for the area of a rectangle is:

Area = length * width

For the top and bottom faces, we have:

Top/bottom area = 4 * 12 = 48 square inches

Finally, we need to find the area of the two slanted faces. These faces are parallelograms, and the formula for the area of a parallelogram is:

Area = base * height

where the base is the distance between the two parallel sides, and the height is the perpendicular distance between the two parallel sides. For the slanted faces, we have:

Slanted face area = 1/2 * (12 + 4) * 10 = 80 square inches

Now we can add up all the areas to get the total amount of wrapping paper needed:

Total area = Front/back area + Top/bottom area + 2 * Slanted face area

Total area = 135 + 48 + 2 * 80

Total area = 343 square inches

Therefore, the minimum amount of wrapping paper needed to cover the package is 343 square inches.

User Eddie Yang
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