Question

A rectangular prism has a length of 12 centimeters, a width of 6 centimeters, and a height of 9 centimeters. A cross section is formed by the prism and a plane that intersects the prism as shown. Find the perimeter of the cross section.

Answer 1

The perimeter of the cross section is 30 centimeters.

Explanation:

In this problem we have the intersection of a rectangular prism an a plane.

The dimensions of the rectangular plane are

`l=12cm\\w=6cm\\h=9cm`

Assuming the plane is cutting the prism horizontally, the cross section would have dimensions

`w=6cm\\l=9cm`

Because only the height would be cut.

So, the perimeter of the rectangle cross-section is

`P_(cross)=2(l+w)=2(6+9)=2(15)=30cm`

Therefore, the perimeter of the cross section is 30 centimeters.