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Title : Rumus Volume Limas terpancung
link : Rumus Volume Limas terpancung

Rumus Volume Limas terpancung

x/t = (b/2)/(a/2)
x/t = b/a
x = b.t/a

h = t – x
h = t – bt/a
h = t(1 – b/a)
h =t(a-b)/a
t = a.h/(a-b)

V bagian bawah = V seluruhnya – Vbagian atas
= 1/3.a2.t – 1/3 b2.x
= 1/3.a2.t – 1/3.b2.(bt/a)
= 1/3.t.(a3-b3)/a
= 1/3.(ah/(a-b)).(a3-b3)/a
= 1/3.(ah/(a-b)).((a-b).(a2+ab+b2)/a
= 1/3.h.( a2+ab+b2)

berikutnya bagai mana membuktikan x/t = (b/2)/(a/2)
Perhatikan segitiga diatas!

Dari segitiga tersebut maka berlaku :
x/t = (b/2) / (a/2).................t= tinggi segitiga keselurahan ( t = x + h)
x/t = b/a. Terbukti...


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