Question

Which shape has 5 faces, 8 edges and 5 vertices? A. triangular pyramid B. rectangular pyramid C. rectangular prism D. triangular prism

Answer 1

C. Rectangular Pyramid

Explanation:

Faces:

A rectangular pyramid has a rectangle as its base. So from it's pinnacle to each of the rectangle's edges, there is a triangular face. As the base has 4 sides, it should have 4 such faces. And the base rectangle is also a face. So it has a total of 5 faces.

So, the number of faces
`$F$` = 5

Edges:

And from its pinnacle to 4 base vertice there are 4 edges. And the base rectangle has four edges. So there are a total of 8 edges

So, the number of edges
`$E$` = 5

Vertice:

The number of vertices
`$V$` must be 5. Becaue we know by Euler's formula
`$V + F - E = 2$` which holds for any shape that doesn't have any hole within it. And 5 is the only value for
`$V$` that satisfies the equation.

So we can conclude that, the shape must have to be rectangular pyramid.

Answer 2

Rectangular Pyramid

Explanation:

Rectangular Pyramid-It has 5 faces, 8 edges and 5 vertices.