Math CentralQuandaries & Queries


Question from oliver, a student:

I need to find out the average height of a specific volume/area.

a standard house shape side walls height 10m, height in centre of house 15m.

width 15m length 25m (the roof spans the width)

Within the house in the corner there is a (box shape) room which is 5m in height by 3m wide and 4 m long

How do i work out the average height of the space directly above the room (same floor area)?


We have two responses for you


Here is my diagram (not to scale)


and you want to find the average height of the orange region.

The average height of this region average of the distances |PQ| and |SR|.



Hi Oliver. The average height of the room would be the height of a simple box with the same floor area. So you need to just find the volume of the house shaped as described, then divide by the floor area.

If you need more help, write back and let us know where you are stuck.

Stephen La Rocque

Oliver wrote back


Yes your diagram is correct I have the distance SR but need to be able to work out PQ. How would I go about this with the info I have provided?




I labeled two more points on the diagram and identified them with dots. What is the slope of the line SA? Can you use this slope to find the distance between B and P?


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