Video: AQA GCSE Mathematics Foundation Tier Pack 2 • Paper 1 • Question 12

a) How many faces does a pentagonal prism have? Circle you answer. [A] 7 [B] 2 [C] 6 [D] 8 b) How many faces of a square based pyramid are squares? Circle your answer. [A] 2 [B] 5 [C] 6 [D] 1

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Video Transcript

Part a) How many faces does a pentagonal prism have? Circle you answer. Is it seven, two, six, or eight. There is also a part b) to this question that we will look at later.

A prism is a solid 3D shape. It has two identical parallel polygon bases. Examples of prisms include cuboids, cubes, and cylinders. If we cut any prism as shown in pink in the diagram, we create exactly the same shape as both ends. In the case of a cylinder, we create a circle. A real-life example of a prism is a Toblerone bar, which is a triangular prism. The diagram in blue is a pentagonal prism. Both ends of the shape are pentagons. And there are five rectangles joining both of the pentagons.

As there are two pentagons and five rectangular faces, we have seven faces in total. This means that a pentagonal prism has seven faces. There is a link between the number of rectangles and the shape at the top and bottom of the prism. A pentagon has five sides. Therefore, there are five rectangles. If we had a hexagonal prism, there would be six rectangles as a hexagon has six sides or edges. Likewise, an octagonal prism would have eight rectangles as an octagon has eight sides or edges.

Part b) How many faces of a square based pyramid are squares? Circle your answer. Is it two, five, six, or one?

A pyramid is a 3D shape whose sides are triangles. They meet at the top of the shape or the apex. The base of the pyramid is a polygon. In this case, it is square based. As already mentioned, each side face of the pyramid is a triangle. In the case of a square-based pyramid, there will be four triangles. The base is a square. Therefore, there are five faces all together.

This question didn’t ask for the total number of faces. It asked us how many of the faces are squares? As there is only one square face in a square-based pyramid, the correct answer is one. A common mistake that is made is to confuse prisms and pyramids. Remember that a prism has two parallel and identical bases whereas a pyramid has only one base and an apex or point at the top.

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