Ask a New Question
Menu

The base of a right rectangular pyramid has length 40 ​cm, width 35 ​cm, and height 11 cm. Describe a cross section that could be formed by a horizontal plane that intersects the faces of the pyramid above the base.

Question content area bottom
Part 1
Which statement below best describes the cross​ section?
A.
An isosceles triangle with base length less than 35 cm and height less than 11 cm.
B.
A rectangle with length greater than 40 cm and width greater than 35 cm.
C.
A rectangle with length less than 40 cm and width less than 35 cm.
D.
An equilateral triangle with base length less than 40 cm and height less than 11 cm.

1 answer

To analyze the situation, we need to consider the geometry of a right rectangular pyramid with a rectangular base. The base of the pyramid has dimensions of 40 cm in length and 35 cm in width, and the pyramid rises to a height of 11 cm.

When a horizontal plane intersects the faces of the pyramid above the base, the resulting cross section will be a rectangle. This is because the horizontal plane will cut through the pyramid parallel to the base, and the shape of the cross section will mirror the base shape, but with reduced dimensions, depending on the height at which the plane intersects.

Given that the height where the cross section occurs is less than 11 cm and that the base dimensions (40 cm x 35 cm) will scale down,

we can conclude that:

  • The length of the cross section will be less than 40 cm.
  • The width of the cross section will be less than 35 cm.

Thus, the best description for the cross section created by this horizontal plane would be:

C. A rectangle with length less than 40 cm and width less than 35 cm.