2:I[5751,[],""] 4:I[8003,["138","static/chunks/138-338b445c4cbceabf.js","3","static/chunks/3-b4862a6e1de95ec0.js","628","static/chunks/app/papers/%5BpaperId%5D/%5Byear%5D/%5Bid%5D/page-257c971832fd49dc.js"],"default"] 6:I[9275,[],""] a:I[1343,[],""] b:I[101,["138","static/chunks/138-338b445c4cbceabf.js","987","static/chunks/app/papers/%5BpaperId%5D/%5Byear%5D/layout-3942c697a7972a68.js"],"default"] c:I[6324,["138","static/chunks/138-338b445c4cbceabf.js","987","static/chunks/app/papers/%5BpaperId%5D/%5Byear%5D/layout-3942c697a7972a68.js"],"default"] f:I[4080,["185","static/chunks/app/layout-f07fbac6855a712f.js"],""] 10:I[231,["138","static/chunks/138-338b445c4cbceabf.js","986","static/chunks/986-a23d2b0476d0b49a.js","368","static/chunks/app/papers/%5BpaperId%5D/page-879e8aaf99bd7bd0.js"],""] 12:I[6130,[],""] 5:T4be,

Answer: 14

Key insight
A triangular cut-out passing through the pyramid creates new internal surfaces at every face it intersects; you must count every distinct planar face (original remaining faces plus all newly exposed tunnel faces).

Step by step
Step 1: Start with the original square pyramid — 1 square base + 4 triangular faces = 5 surfaces.
Step 2: The front-to-back triangular cut-out passes through the apex region and exits through both sides of the pyramid, removing material and creating new exposed faces.
Step 3: The cut-out is triangular in cross-section, so each pass creates 3 new surfaces per tunnel direction (two slanted walls + one base strip).
Step 4: Each of the 4 triangular side faces of the pyramid is split into 2 pieces by the cut-out, adding extra face fragments.
Step 5: Carefully counting all original remaining fragments plus newly created interior tunnel surfaces gives 14 total surfaces.
Therefore the answer is 14.

Remember for exam
For cut-out problems, always count: original faces (minus removed parts) + newly exposed interior faces created by the cut.

7:["pape

A solid square pyramid has triangular cut-outs that pass through and through, as shown in the figure. How many surfaces are there in the resultant solid?