Video: Pack 3 • Paper 3 • Question 5

Pack 3 • Paper 3 • Question 5

02:24

Video Transcript

The diagram shows a prism with a cross section of an irregular pentagon. On the grid below, draw the front elevation and the side elevation of the prism. Use a scale of one square to four meters.

We can work out the number of squares that correspond to each of the four lengths by dividing by four, as one square is equal to four meters. 24 meters will be equal to six squares, as 24 divided by four is equal to six. In the same way, 16 meters will be equal to four squares. 14 meters will be equal to three and a half or 3.5 squares. And eight meters will be equal to two squares.

We now need to consider what we would see on the front elevation of the prism. The bottom half of the front elevation would be a rectangle, six squares across and two squares up. Above this, we would see another rectangle, which would represent the sloping roof. This would also be six squares wide, but this time 1.5 or one and a half squares high. This means that the full front elevation will be a rectangle, six squares across and 3.5 squares up. Six squares is equal to 24 meters. And three and a half or 3.5 squares is equal to 14 meters, the height of the prism.

If we now consider the side elevation, it is clear that we would see a pentagon. The pentagon would be four squares wide, as four squares is equal to 16 meters. We would then have two parallel sides going up two squares. This represents the eight meters.

Finally, we would have two equal-length diagonal sides that would give a total height of the pentagon of 3.5 squares, as 3.5 squares is equal to 14 meters. The front elevation of the prism consists of two rectangles making a larger rectangle. And the side elevation consists of a pentagon.