Starting at the top, if you cut a square pyramid in half using a single cut, what is the shape of the newly-exposed section?
1. C
2. A
3. C
4. D
5. A
6. B
7. C
8. C
9. Word pad
100
@Hal
100% Thanks! I had this as an overdue and was too lazy to do the actual work. I always do my work without help but this time i was lazy! But thx!
THANK YOU SO MUCH HAL. THANK YOU
vertical cross-sections are triangles
horizontal cross-sections are squares
there is 8 (now)
but hey correct
To determine the shape of the newly-exposed section when a square pyramid is cut in half using a single cut, let's break down the process step by step:
Step 1: Understand the Pyramid
A square pyramid has a square base and four triangular faces that meet at a single point, called the apex or vertex.
Step 2: Visualize the Cut
Imagine making a single cut through the pyramid, starting from the apex and extending down towards the base. This cut bisects the pyramid into two halves.
Step 3: Examine the Cut Section
The shape of the newly-exposed section depends on where the cut intersects the pyramid. There are three possible cases:
Case 1: The Cut Intersects the Apex
If the cut passes directly through the apex of the pyramid, then the newly-exposed section will be a triangle. This triangle will have one side equal in length to the distance from the apex to any corner of the base, and the other two sides will be equal in length.
Case 2: The Cut Intersects an Edge of the Base
If the cut intersects one of the edges of the square base, then the newly-exposed section will be a trapezoid. This trapezoid will have a parallel side equal in length to the side of the square base that the cut intersects. The other parallel side will be shorter, and the remaining two sides will be slanted.
Case 3: The Cut Intersects the Center of an Edge of the Base
If the cut passes through the center of one of the edges of the square base, then the newly-exposed section will be a pentagon. This pentagon will have two opposite sides parallel and equal in length to half the length of the side of the square base. The remaining three sides will be unequal, with two shorter sides and one longer side.
So, the shape of the newly-exposed section when a square pyramid is cut in half using a single cut depends on where the cut intersects the pyramid: triangle, trapezoid, or pentagon.