FTCE General Knowledge Math Practice Test

Which geometric figure has faces formed entirely by triangles and at least one triangular base?

1. Tetrahedron

2. Pyramid

3. Cylinder

4. Sphere

The correct answer is: Pyramid

The correct answer is a pyramid. A pyramid is defined as a three-dimensional geometric figure that has a polygonal base and triangular faces that converge to a single point known as the apex. Since one of its bases is a triangle (in the case of a triangular pyramid), all the faces in this shape are indeed formed by triangles, satisfying the condition stated in the question. In contrast, a tetrahedron also meets the criteria of having faces formed entirely by triangles, but it's a specific type of pyramid with a triangular base and three additional triangular faces. The term pyramid is more general, as it can refer to various base shapes—including triangles, squares, and other polygons. The cylinder is not applicable because it has circular bases and curved surfaces, thus not having any triangular faces. Similarly, a sphere has no faces and is a perfectly round three-dimensional shape. Consequently, both of these options are not relevant to the question. The general definition of a pyramid encompasses a variety of shapes, making it the most appropriate answer in this context.