Question

PLS HELP! i rly need help on this. it’s hard for me.

Answer 1

Answer:

The 3D solid shown in the image is a hexagonal pyramid. If we made a cross section with a vertical slice (top to bottom), we would have an isosceles triangle.

Useful Extra Knowledge:

However—and this isn't a question here, but just useful knowledge—if we made a cross section with a horizontal slice (left to right or right to left), we would have a regular hexagon. If it were a diagonal cross section, we would have an irregular hexagon.

Step-by-step explanation:

First, what's the difference between a sphere, a cylinder, a pyramid, a cone, and a prism? These are all 3D solids, but in your case, an explanation of what they are may be a good refresher:

• A sphere is a 3D solid where every point is equidistant from the center point. Basically, it's a 3D circle. It's completely round.
• A prism is a 3D solid with straight, parallel sides and a polygonal base.
• A cylinder is a 3D solid with straight, parallel sides and a circular base
• A pyramid is a 3D solid with sides that converge at a common vertex and a polygonal base.
• A cone is a 3D solid with sides that converge at a common vertex and a circular base.

We definitely know this shape can't be a sphere! It's not completely round! Actually, take a closer look: there's no hint of a circle anywhere in the figure. It can't be a cylinder nor a cone.

This means it's either a pyramid or a prism. But, going back to the definitions above, let's redefine the difference between the two: pyramids have only one base and only triangular faces, while prisms have two bases and rectangular faces.

How many bases does this figure have? It has one base. And what shape are its faces? They're all triangles! This means we have to be looking at a pyramid.

So, you may think, that solves it. We're looking at a pyramid.

Sorry, buddy. It's not that easy. We can classify this figure even further. How do we do this? We use its base! And what type of polygon is the base? When we count the sides of the base, we find six sides, which means this shape is a hexagon. So this is a hexagonal pyramid, right?

Actually, there's one more specification we could give this. That hexagon has sides that are all equal to each other. That may not seem special to you, but there's a special term given to polygons who have equal sides and equal inner angles: they are called regular polygons.

That description matches the base of our shape, right? So, now we have the name of the figure: it's a regular hexagonal pyramid.

Now, what about the cross section? This means we're taking a piece of that solid, like cutting into a cake with a knife. Who likes cake here?

I digress. This piece, the cross section of the 3D solid, becomes a 2D shape. Now, the question asks for the shape of a vertical cross section, which means up and down, like the y-axis on the coordinate plane/Cartesian plane.

So, imagine taking a butter knife and slicing right down the middle of that bad boy. If you get the middle point exactly, you'll have two equal halves which would look like triangles with two equal sides: an isosceles triangle.

That's assuming you look straight on at them. If you veered to the side a little, you'd find a scalene triangle (a triangle with no equal sides).

But, should you miss the center a little, you'd get a trapezoid instead, because part of the top would be missing.

But I'm assuming the question is asking about a vertical slice exactly down the middle and viewed straight on. In that case, your answer is an isosceles triangle.

I droned on for a bit, I know. But hopefully this helps you understand the concept better! Have a great day!