Rghv9906 wrote:
KarishmaB wrote:
divya517 wrote:
But i could not interpret the shape from original diagram given in the question
You can ignore the diagram completely (as I did when I solved it) because the question tells you that you get a figure with "2 pyramids each with a square base that they share". Imagine what one pyramid looks like - a square with triangles attached to each side and the tips of the triangles stuck together. Imagine how would you have two pyramids with a common base. There would be 4 triangles on the lower side of the square too and their tips would be stuck together. So in all, the figure would have 8 faces (4 triangles + 4 triangles) and 12 edges ( 4 edges where the top triangles join, 4 edges where the bottom triangles join and 4 edges of the square).
All in all you will have 8 + 12 = 20 faces + edges
But why are the face and edges of the base not considered?
Hello
Rghv9906,
The edges of the base are considered, but the base has
no face to consider. Let me first help you visualize the figure in a slightly different way. Then, we will come to faces and edges one by one.
VISUALIZE - Consider a pyramid with no base but just 4 faces and 4 edges.
- To help you visualize, here’s another idea - think of a hollow cone with no base; it is like a birthday cap. Now, just change the curved surface of the base into 4 triangular faces joined to each other along 4 edges.
- Now, consider another such pyramid and finally join them both by taping together the edges along the base of each pyramid. You will form the geometrical figure given in the question.
FACES - Observe how each of our pyramids has 4 faces (with the base, the no. of faces would have been 5).
- This way, the two pyramids joined will have 8 faces.
You were worried about the common base of these pyramid. And see how in this visualization, there is no such base anyway!
Important - I presented this in a way that you do not get confused about the face forming each pyramid’s base. But you still need to understand that even in Karishma’s visualization, the common square base would just be completely enclosed by the two pyramids coming together. There would be nothing visible outside the geometric figure we have in this question. And so, you still would not consider it.
EDGES - Recall that the 4 faces of each pyramid were joined by 4 edges.
- This already gives us 4 × 2 = 8 edges in total from both the pyramids. -------(1)
- Now, where the bases of the two pyramids are joined, we have 4 more edges. --------(2)
- In total we have 8 + 4 = 12 edges.
Note: Even though each pyramid had 4 edges in its base, we took only one set of 4 edges and not two sets. This is because we joined the bases of the two pyramids and had one common base only.
TAKEAWAY Only faces and edges visible from the outside of a geometric figure are considered.
Hope this helps!
Best Regards,
Ashish Arora
Quant Expert,
e-GMAT
close
03 Aug 2021, 01:22
