Follow the rules for working with measurements. Two different sizes of square metal duct are joined by a piece that is a frustum of a pyramid. Find the lateral surface area, if the small end is square with one side of length 17 in. and the larger square end is of length 19 in. on one side with a slant height of 2 in. A) A = 141 in. ² B) A = 288 in. ² C) A = 144 in. ² D) A = 151 in. ² E) A = 132 in. ²

Question

Quizplus · Accepted Answer

The lateral surface area of the frustum of the pyramid can be found using the formula:
Lateral surface area = (slant height / 2) * (perimeter of the two bases)
The perimeter of the smaller square base is 4 * 17 = 68 in.
The perimeter of the larger square base is 4 * 19 = 76 in.
The average perimeter of the two bases is (68 + 76) / 2 = 72 in.
Using the Pythagorean theorem, we can find the height of the frustum:
(2 in.)^2 = (19 in. - 17 in. + h)^2 + (h)^2
4 = h^2 + (h + 2)^2
4 = 2h^2 + 4h + 4
0 = 2h^2 + 4h
0 = h(h + 2)
h = 0 or h = -2 (discard the negative solution)
Therefore, the slant height of the frustum is h = 2 in.
Plugging in these values to the formula, we get:
Lateral surface area = (2 / 2) * 72 = 72 in.
Therefore, the best choice is C.

Follow the Rules for Working with Measurements