Question

a plane slices through a square pyramid parallel to its base. what is the shape of the cross section? the cross section is a dropdown with options: right triangle, parallelogram, square, trapezoid

Explanation:

Step1: Analyze the base of the pyramid

The base of a square pyramid is a square, meaning all its sides are equal and all angles are right angles.

Step2: Consider the plane slicing parallel to the base

When a plane slices a three - dimensional figure parallel to its base, the cross - section will have the same shape as the base (in terms of the type of polygon, with proportional dimensions). Since the base is a square, the cross - section formed by a plane parallel to the base should also be a square. Let's analyze the other options:

• A right triangle: A plane parallel to the square base of a pyramid will not form a triangle, as the intersection with the lateral faces (which are triangles) when parallel to the base will create a quadrilateral.
• A parallelogram: While a square is a type of parallelogram, the more specific and correct shape here is a square because of the properties of the square pyramid's base and the parallel slicing.
• A trapezoid: A trapezoid has only one pair of parallel sides. But when slicing parallel to the square base, both pairs of opposite sides of the cross - section will be parallel (same as the base), so it's not a trapezoid.

Answer:

square (from the options, the correct option is the one labeled "square")