Select the cross-section that results from slicing a rectangular pyramid.
The pyramid is sliced in a way such that the plane passes through the middle of the pyramid in a direction perpendicular to the base.
A. The cross-section is a triangle.
B. The cross-section is a trapezoid.
C. The cross-section is a rectangle.
D. The cross-section is a square.
I think its A or D
Well, you might say the pyramid is getting sliced like a sandwich. Now, imagine the perfect slice that passes through the middle of the pyramid. If you were to take a bite of it, would you end up with a triangular-shaped mouthful or a square-shaped one?
I hate to be the bearer of bad news, but it seems a triangular bite is off the menu. So, D can be crossed off the list.
And with that, we arrive at the correct answer! It's C, my friend! The cross-section resulting from slicing a rectangular pyramid is a rectangle. It's like taking a slice out of the pyramid and revealing its rectangular core. Bon appé!
The correct answer is A. The cross-section that results from slicing a rectangular pyramid in a way that the plane passes through the middle of the pyramid in a direction perpendicular to the base is a triangle.
To determine the correct choice, let's break down the problem and analyze the options.
A rectangular pyramid has a rectangle as its base and triangular faces that meet at a common vertex. When we slice a rectangular pyramid with a plane passing through the middle of the pyramid in a direction perpendicular to the base, the resulting cross-section is parallel to the base and will be the same shape as the base.
Given that the base of the rectangular pyramid is a rectangle, we can eliminate option A (a triangle) and option D (a square), as they do not match the shape of the base.
This leaves us with two options: B. The cross-section is a trapezoid and C. The cross-section is a rectangle.
To determine which choice is correct, let's consider the definition and properties of a trapezoid and a rectangle.
A trapezoid is a quadrilateral with one pair of parallel sides. In this case, since the cross-section is parallel to the base of the pyramid, we know that the cross-section will have two pairs of parallel sides. Therefore, option B is incorrect because a trapezoid does not have two pairs of parallel sides.
On the other hand, a rectangle is a quadrilateral with all four angles equal to 90 degrees and opposite sides that are congruent and parallel. Since the base of the rectangular pyramid is a rectangle, the cross-section resulting from the slice will also be a rectangle. Thus, option C is the correct answer.
Therefore, the correct choice is:
C. The cross-section is a rectangle.
since it passes through the vertex, it will have to have a point.
A is your best bet.