Apedestal 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 squared of burlap cloth
to cover the lateral area of the pedestal. find the height of the pedestal.

Given:
side lengths of right triangles = 12 cm ; 16 cm ; 20 cm
lateral area = 192 cm²

lateral area of a triangular prism = perimeter * height
192 cm² = (12 cm + 16 cm + 20 cm) * height
192 cm² = 48 cm * height
192 cm² / 48 cm = height
4 cm = height

The height of the pedestal in the shape of a triangular prism is 4 cm.