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.