Thread: geometry

A rectangular room 4m by 3m and 2m high. A Snail is at A and wants to get to R. Find the shortest path it could crawl without crossing the ceiling. Find the length of this path and draw it on a 3D sketch of the room.

Your group has decide, with great wisdom, that it's strategy is to imagine the room is a box with the edges cut so that it lays flat. On sketches of the fattened room, plot possible pathways and calculate the distances covered by the Snail along these pathways.

The ant is not allowed to use rhe ceiling PQRS.

a) Trial 1.
Cut the box such so that you can lay/spread where a portion is like so:
It's a horizontal rectangular diagram whose bottom side is ABQPA and whose top side is DCRSD. D is directly above A, C above B, R above Q, S above P, D above A.
The ant would travel a straight line from A to R.
By Pythagorean theorem,
distance, d^2 = (AB +BQ)^2 +(QR)^2
d = sqrt[(4 +2)^2 +(3)^2] = sqrt(45) = 6.708 meters --------**


a) Trial 2.
Cut the box such so that you can lay/spread where a portion is like so:
It's a vertical rectangular diagram whose left side is ADSPA and whose right side is BCRQB. B is to the right of A, C of D, R of S, Q of P, B of A.
The ant would travel a straight line from A to R.
By Pythagorean theorem,
distance, d^2 = (AB)^2 +(BC +CR)^2
d = sqrt[(4)^2 +(3 +2)^2] = sqrt(41) = 6.403 meters --------**