# Video: GCSE Mathematics Foundation Tier Pack 3 • Paper 3 • Question 9

GCSE Mathematics Foundation Tier Pack 3 • Paper 3 • Question 9

01:51

### Video Transcript

Here is the parallelogram 𝐴𝐵𝐶𝐷. Part a) On the diagram, mark the angle 𝐵𝐶𝐷 with the letter 𝑥.

One of the mathematical conventions for labelling angles is to use three letters. The middle letter is always the letter that describes the vertex at which the angle is situated. The first and last letters give you a path to follow. Let’s see what this looks like.

The path we want to follow starts at 𝐵 and then goes to 𝐶 then back out to 𝐷 again. The angle 𝐵𝐶𝐷 sits at the vertex 𝐶. So it’s this one labelled 𝑥.

Here is the square-based pyramid 𝑃𝑄𝑅𝑆𝑇. Part b) Shade the face 𝑃𝑅𝑆.

In geometry, the word “face” is used to describe one of the flat surfaces on a 3D shape. In this shape, there are triangular faces and a square face. The face 𝑃𝑅𝑆 is the triangle enclosed by these three letters.

Like we did with the angles, we start at 𝑃, go to 𝑅, then from 𝑅 to 𝑆. And since it is a triangle, back again from 𝑆 to 𝑃. We can then shade the face 𝑃𝑅𝑆, as shown.

Part c) How many faces does a square-based pyramid have?

We said that the pyramid has some triangular faces and a square face. The square face sits at the base of the pyramid; that’s the first face. Since the square has four sides and the triangular faces come off of each of these sides, there must be four triangular faces. One plus four is five; that’s a total of five faces.