Final answer:
To calculate the surface area of the given geometric shape with dimensions x=6 in, y=8 in, and z=10 in, you apply the surface area formula for a rectangular prism, leading to a total surface area of 376 square inches.
Step-by-step explanation:
The question at hand involves the calculation of the surface area of a 3-dimensional geometric shape given the dimensions x = 6 in, y = 8 in, and z = 10 in. This task requires applying knowledge of geometric formulas. The fact that dimensions are provided for three different measures suggests that the shape could be a rectangular prism. The surface area of a rectangular prism is calculated by finding the area of all six faces (2lw + 2lh + 2wh) and summing them together, where l is the length, w is the width, and h is the height of the prism.
Given x = 6 inches (width), y = 8 inches (height), and z = 10 inches (length), we can substitute these measures into the rectangular prism surface area formula: Surface area = 2(10 in * 6 in) + 2(10 in * 8 in) + 2(6 in * 8 in). Calculating these areas, we get Surface area = 2(60 in²) + 2(80 in²) + 2(48 in²), which leads to 120 in² + 160 in² + 96 in² = 376 in². So, the surface area of the shape is 376 square inches.