# The New Apprentice

An apprentice went to a new building to measure the CHB wall area to be painted. He is equipped with Laser Distance Meter that measure the distance from that device to a wall (by means of reflected beam). The doors are of standard dimension while the ceilings are of same height. He started taking measurements 'inside' the building using the device. Unfortunately, the battery ran out after his 5th measurements and the area must be submitted to his boss soon. Nevertheless he used his acquired measurements to be able compute for the total CHB area.

Which measurements did he took? (pls. draw in above plan)

• CHB (Concrete Hollow Block) wall are the white lines. – TSLF Nov 2 '16 at 16:59
• Does he know the ceiling height or does he have to acquire it from measurements? – Verence Nov 2 '16 at 17:08
• @Verence-No, that is one of the measurements. Right question. – TSLF Nov 2 '16 at 17:11
• Is glass simply invisible to the distance meter? – Gareth McCaughan Nov 2 '16 at 17:11
• @GarethMcCaughan- Yes refraction dont affect the reading – TSLF Nov 2 '16 at 17:13

The numbers show the measurements starting points. The fifth measurement is the ceiling. The Roman numbers mark the segments whose lengths (only sum of them, not the lengths themselves) are obtained after the measurement. I've put "splitting" marks on some walls for convenience so that segments visually go in pairs. The final formula is (2*l1 + l2 + 2*l3 + 2*l4)*l5

• Nicely drawn. Also possibly (technically) need to subtract 6x(area of a door) in the final formula. – Dan Russell Nov 2 '16 at 17:40
• @DanRussell Of course. – Verence Nov 2 '16 at 17:47
• @DanRussell Actually it's 10x(area of a door). ;) – Sleafar Nov 2 '16 at 20:07
• @Sleafar Precisamundo. – Dan Russell Nov 2 '16 at 20:16

[EDITED to add:] Note that this is a wrong answer. I believe Verence's is right; in particular it uses the right cheeky trick to overcome what at first looks like an insuperable difficulty.

He measured

the height of the ceiling (h); the distance from west of dining area to "middle" of cuisine (x1); the distance from west of cuisine to east of cuisine (x2); the distance from south of cuisine to north of reception (y1); the distance from south of exclusive to north of exclusive (y2).

Then

the total length of east-west wall is $2(x_1+x_2)$ and the total length of north-south wall is $2(y_1+y_2)$ and so the total area of wall is $2h(x_1+x_2+y_1+y_2)$.

• Does this depend on the office y dimension being a specific fraction of the exclusive y dimension? I can't see how the office is being counted – Angzuril Nov 2 '16 at 17:28
• You missed some parts. The reception part to the west of the glass partition isn't covered by X measurement, and the office east wall isn't covered by Y measurement. – Verence Nov 2 '16 at 17:29
• @Verence Damn, you're right. – Gareth McCaughan Nov 2 '16 at 17:31
• ... Yeah, I can -- but y'know what?, it doesn't really contribute anything beyond Verence's answer, so I'll just leave this here being wrong. Apologies. – Gareth McCaughan Nov 2 '16 at 17:44
• The infallible and prodigious GarethBot makes a pre-programmed mistake designed to convince the rest of us that it is fallible and not a bot at all. ;) – Dan Russell Nov 2 '16 at 17:54