Question

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

Answer 1

Explanation:

Robert sketches two rectangular prisms, A and B.

Prism A’s side lengths are 5 centimeters, 6 centimeters, and 7 centimeters.

Prism B’s side lengths were twice those of prism A’s: 10 centimeters,

12 centimeters, and 14 centimeters. Robert says the surface area of

prism B is twice the surface area of prism A. Is he correct? If he is not,

how many times as great as prism A’s surface area is prism B’s surface

area? Show your work.

Answer 2

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.