Final answer:
The area of the cross section formed by the diagonal cut across the base of the cheese is 60 square centimeters, which is calculated using the area formula for a triangle.
Step-by-step explanation:
A rectangular piece of cheese measuring 8 cm in width, 15 cm in length, and 6 cm in height is cut perpendicular to and diagonally across the base. To find the area of the cross section formed by the cut, we need to determine the dimensions of the resulting triangular cross section. Since the cut is diagonal, the length of the base of the triangle will be equal to the cheese's 15 cm length, and the height of the triangle will be the same as the cheese's width, which is 8 cm.
Using the formula for the area of a triangle, which is 1/2 × base × height, we can calculate the area:
- Area = 1/2 × 15 cm × 8 cm
- Area = 7.5 cm × 8 cm
- Area = 60 cm²
Therefore, the area of the cross section is 60 square centimeters, which does not match any of the given options (A) 138, (B) 102, (C) 150, (D) 90. It appears there might be an error in either the problem statement or the provided answer choices.