a plane intersects a square pyramid perpendicular to its base but not through a vertex.The plane forms a cross section what is the shape of the cross section
a)trapezoid
b)triangle
c)square
d)rectangle
its a trapezoid.
To determine the shape of the cross-section formed by a plane intersecting a square pyramid, perpendicular to its base but not through a vertex, we can visualize the three possible options: a trapezoid, a triangle, or a rectangle. Let's consider each case:
a) Trapezoid: If the plane intersected the pyramid in such a way that the cross-section had four sides, with two sides parallel and two sides non-parallel, then the cross-section would be a trapezoid.
b) Triangle: If the plane intersected the pyramid in such a way that the cross-section had three sides and all three sides were non-parallel, then the cross-section would be a triangle.
c) Square: Since the plane does not intersect through any of the pyramid's vertices, forming a square cross-section is not possible. Therefore, we can eliminate this option.
d) Rectangle: If the plane intersected the pyramid in such a way that the cross-section had four sides, with two parallel sides and two non-parallel sides, then the cross-section would be a rectangle.
Considering the given conditions, the only shape that satisfies the criteria is a rectangle (option d). Therefore, the shape of the cross-section formed by the plane intersecting the square pyramid described is a rectangle.
planes that intersect only one of the edges are triangular.
Planes that contain two of the edges have quadrilateral cross-sections. If the plane is parallel to one of the base edges, the section is a trapezoid. Otherwise, it is just a general quadrilateral.
Try drawing some cases.