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设 S1的高为 h1, S2的高为 h2
S1=(P+Q)h1/2 S2=(Q+R)h2/2
S1=S2 (P+Q)h1/2 =(Q+R)h2/2 h1/h2= (Q+R)/(P+Q)
S=(P+R)(h1+h2)/2=(P+Q)h1/2 +(Q+R)h2/2
(P+R)(h1+h2)=(P+Q)h1+(Q+R)h2
(P+R)h1+ (P+R)h2=(P+Q)h1+(Q+R)h2
(P+R)h1-(P+Q)h1 = (Q+R)h2 -(P+R)h2
(R-Q)h1=(Q-P)h2 h1/h2=(Q-P)/(R-Q)= (Q+R)/(P+Q)
(Q-P)(P+Q)= (Q+R)(R-Q) Q^2-P^2=R^2-Q^2
P^2+R^2=2Q^2
S1=(P+Q)h1/2 S2=(Q+R)h2/2
S1=S2 (P+Q)h1/2 =(Q+R)h2/2 h1/h2= (Q+R)/(P+Q)
S=(P+R)(h1+h2)/2=(P+Q)h1/2 +(Q+R)h2/2
(P+R)(h1+h2)=(P+Q)h1+(Q+R)h2
(P+R)h1+ (P+R)h2=(P+Q)h1+(Q+R)h2
(P+R)h1-(P+Q)h1 = (Q+R)h2 -(P+R)h2
(R-Q)h1=(Q-P)h2 h1/h2=(Q-P)/(R-Q)= (Q+R)/(P+Q)
(Q-P)(P+Q)= (Q+R)(R-Q) Q^2-P^2=R^2-Q^2
P^2+R^2=2Q^2
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