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------------------------------------------------ A pedestal in a craft store is in the shape of a triangular prism. The bases are right triangles with side lengths of 12 cm, 16 cm, and 20 cm. The store owner used 192 cm$^2$ of burlap cloth to cover the lateral area of the pedestal.

Find the height of the pedestal.

The height of the pedestal, which is a triangular prism with bases that are right triangles with side lengths of 12 cm, 16 cm, and 20 cm, is found to be 4 cm based on the given lateral area of 192 cm squared.

Explanation:

To find the height of the pedestal, we first recognize that the given side lengths of the base form a right triangle, where 12 cm and 16 cm can be considered as the perpendicular sides and 20 cm as the hypotenuse.

This is confirmed by the Pythagorean theorem (122 + 162 = 202).

The lateral area of a triangular prism is calculated by multiplying the perimeter of the base triangle by the height (H) of the prism.

Since the perimeter of the base triangle is 12 cm + 16 cm + 20 cm = 48 cm, and the given lateral area is 192 cm², we find the height by dividing the total lateral area by the perimeter of the base.

Therefore, H = 192 cm² / 48 cm = 4 cm. Hence, the height of the pedestal is 4 cm.