Final answer:
To find the height of the frustum of the pyramid, you can use the formula for the volume of a frustum. Given the areas of the upper and lower bases and the volume, you can substitute these values into the formula and solve for the height. The height of the pyramid is approximately 2.866 units.
Step-by-step explanation:
To find the height of the frustum of the pyramid, we can use the formula for the volume of a frustum, which is given by:
V = (1/3)h(A1 + A2 + sqrt(A1A2)), where V is the volume, h is the height, and A1 and A2 are the areas of the upper and lower bases respectively.
Given that the volume is 42 cubic units, A1 = 12 sq. units, and A2 = 42 sq. units, we can substitute these values into the formula and solve for h:
42 = (1/3)h(12 + 42 + sqrt(12 * 42))
42 = (1/3)h(12 + 42 + 6√14)
126 = h(54 + 6√14)
126 = 54h + 6h√14
72 = 6h(9 + √14)
12 = h(9 + √14)
h = 12/(9 + √14)
Therefore, the height of the pyramid is approximately 2.866 units.