A rectangular pyramid is sliced such that the cross section is perpendicular to its base and the cross section does **not** intersect its vertex.

What is the shape of the cross section?

When a rectangular pyramid is sliced by a plane perpendicular to its base, and the plane does **not** intersect the vertex, the shape of the cross section is a **trapezoid**.

### Explanation:
- A rectangular pyramid has a rectangular base and four triangular faces that meet at a single vertex.
- When the slicing plane is perpendicular to the base and does not pass through the vertex, it intersects the two opposite triangular faces and the base. 
- Since the plane cuts across two sides of the rectangular base at different heights (assuming the cut is parallel to the base and at a distance from the vertex), the two resulting edges of the cross section will be parallel to each other (corresponding to the opposite sides of the rectangle).
- The other two edges of the cross section will be slanted, connecting these parallel edges, forming a trapezoid.

Would you like more details on any part of the explanation?

---

**5 Related Questions:**
1. What happens to the cross section if the slicing plane is parallel to the base?
2. How does the cross section change if the pyramid has a triangular base?
3. What is the cross-sectional shape if the slice passes through the vertex?
4. How can you determine the area of the trapezoidal cross section?
5. What other 3D shapes have trapezoidal cross sections when sliced similarly?

**Tip:** Visualizing a 3D object and the plane slicing it can help you understand the resulting 2D cross section shape.

Explore the shape of cross sections when a rectangular pyramid is sliced perpendicular to its base without intersecting its vertex. Learn about the resulting trapezoid shape and how it forms from the geometry of rectangular pyramids. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation