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Q: What is the name of the 3d shape that has a square base and four other sides which are triangles?

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The base is a square, while the four sides are all triangles.

One square or rectangle as it's base, and the other sides are triangles.

A pyramid. The square being the base and the triangles the 'sides' - each having a side connected to a side of the square - the other sides connected to 'neighbor-triangles'.

There are 4 triangles that make up a pyramid. 4 on the sides and on the bottom a square or rectangle.

A square * * * * * No, the shape is equilateral. You can have equilateral triangles, 4-sided shapes such as rhombi, or polygons with 5 or more sides. A square is just one specific example.

triangles square

Yes. Consider the situation when: the right-angled triangles are also isosceles and the hypotenuse (longest side) of the triangles is equal to the side of the square. If you surround a square with four of right-angled triangles (the sides of the square being in contact with the hypotenuses of the triangles), you get a larger shape which is also a square. Taking this as a basic unit, you can make a tesselations. You can also make tessalations if you have two sets of squares, one with sides the same length of the hypotenuse of the triangles and one with sides the same length as the smaller sides of the triangles.

The same as other pyramids -- 5. 4 triangles and one square.

A pentagon

A regular octahedron - two square based pyramids stuck together along their square bases.

triangles

shape and sizecorresponding sides

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