A pedestal in a craft store is in the shape of a triangular prism. The bases are right triangles with side lengths of 12 centimeters, 16 centimeters, and 20 centimeters. The store owner wraps a piece of rectangular cloth around the pedestal but does not cover the identical bases with cloth. The area of the cloth is 192 square centimeters.

1. What is the distance around the base of the pedestal? How do you know?
2. What is the height of the pedestal? How did you find your answer?

The distance around the base of the pedestal, which is the perimeter of the base triangle, is 48 cm. The height of the pedestal is found by dividing the area of the cloth by the perimeter of the base triangle, yielding a height of 4 cm.

To find the distance around the base of the triangular prism pedestal, which is essentially the perimeter of the base triangle, we add up its side lengths. Since the base is a right triangle with sides measuring 12 cm, 16 cm, and 20 cm, the perimeter P is straightforwardly calculated:

P = 12 cm + 16 cm + 20 cm = 48 cm.

The cloth covers the lateral surface of the prism, which is a rectangle, and its area is given as 192 square centimeters. The area (A) of a rectangle is calculated by A = length * width. Here, the length corresponds to the perimeter of the base triangle (P), and the width corresponds to the height (H) of the prism. Therefore, we can find the height of the pedestal by re-arranging the formula for area (A = P * H) to solve for H:

H = A / P = 192 cm2 / 48 cm = 4 cm.

So, the height of the pedestal is 4 centimeters.