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Hard question

My house has an attic consisting of a horizontal rectangular base of length 2q and breadth 2p, (where p

My house has an attic consisting of a horizontal rectangular base of length 2q and breadth 2p, where p

Something wrong with the website it keeps showing only a bit of the question.

Anyway it's step 1994 paper 1 q1

Help please

The full question is: My house has an attic consisting of a horizontal regular base of length $2q$ and breadth $2p$ (where $p < q$) and four plane roof sections each at angle $\theta$ to the horizontal. Show that the length of the roof edge is independent of $\theta$ and find the volume of the attic and the surface area of the roof.

Drawing a diagram is your best bet here. Since all the sections are inclined at the same angle, the roof ridge will be central. From your diagram, can you use trigonometry to find the height $h$ of the roof? Once that's done, it shouldn't be too much more work to find the length of the roof ridge in terms of $p$ and $q$, you'll find that $\theta$ disappears. Post your workings if you're still unsure about what's going on.

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Underground Mathematics: Selected worked STEP questions

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University of Cambridge Mathematics Faculty: What do we look for?

University of Cambridge Mathematics Faculty: Information about STEP

University of Cambridge Admissions Office: Undergraduate course information for Mathematics

Stephen Siklos' "Advanced Problems in Mathematics" book (external link)

MEI: Worked solutions to STEP questions (external link)

OCR: Exam board information about STEP (external link)

AMSP (Advanced Maths Support programme): Support for University Admission Tests (external link)