由 Raceleader 於 星期四 四月 10, 2003 8:59 am
Let O be the Centroid of base triangle ABC, the apex is D:
We can draw AO to cut BC at E
By congruent triangle, we get that ∠AEB=∠ AEC=90°
By Pythagoras, we get AE=√3/2
Since O is the centroid, so AO:OE=2:1
So, OA=√3/3
We get that base area = (1/2)(AE)(BC) = √3/4
By Pythagoras Theorem:
DO2+OA2=AD2
DO2+1/3=1
DO= √(2/3)
So, the volume = (1/3)(Base area)(height)=√2/12