hi demha,

Glad you enjoyed our discussion about these problems. We have identified a big error with the work that Compu High are teaching you. The teaching page is available as a 'demo' so I have been able to read it all. The volume calculations are fully correct but the slant height section is WRONG.

Because I am a teacher of maths, I cannot just let you do these questions without showing you the correction. I'll do that first. Then you'll want to get their answers so you get full marks. That's OK. I have used their method and Q6 to Q10 all have a 'correct' answer. So hopefully, at the end, you will understand the work properly and be able to get full marks. I would just add, this is not the only criticism I have of this on-line course but I won't burden you with all my objections. Let's get on.

Correction: If you buy some wire so you can make a wire-frame version of these pyramids, you could proceed as follows. (see diagram)

(i) Cut two lengths **a** and two widths **b**. Join them to make the base rectangle.

(ii) Join the diagonals to find the middle and make a temporary wire for the height **h**. This fixes the vertex.

**At this point the five points of the pyramid are all fixed.**

(iii) You can cut four wires to join the base to the vertex and the model is complete.

**It is not necessary is say how long the red lines for the slant heights are because they are already there, whatever size they need to be to join the midpoints of the base to the vertex.** Just choosing a length for these red lines is not an option. Their lengths can be calculated using Pythagoras' theorem. Furthermore, with a rectangular base the two slant heights will not be the same, so giving a single slant height value is only possible where the base is a regular polygon. A rectangle is not a regular polygon.

This is why I have had such a problem with the slant height values given. The pyramids described cannot exist because those slant height values won't work!

Sorry for the rant, but I felt I had to get that off my chest. I feel better. If that's leaving you worried and confused I apologise, but I have to take account of the possibility that other members of the forum may be reading this thread and I don't want them being taught incorrectly.

So now, back to the problems. You can, of course, ignore all I have just said, and concentrate on getting the 'right' answers. (Anyway, once you have a volume, you'll know which answer to choose, without having to calculate the lateral areas at all. This is another criticism whoops, I'd better move on!)

The formula for the volume is

You have done Q6 volume correctly.

Their formula for lateral area is

So what you need to do is

(i) Add a + b + a + b to get the perimeter (distance around the base).

(ii) Calculate 1/2 of this and multiply by the slant height.

You can be fairly confident you have the right result if you can choose a single multi-choice answer that fits both the volume and area you have worked out.

Good luck.

Bob