PI*[(a+b)/2]²-PI(a/2)²-PI(b/2)²,怎么计算,越详细越好.PI是匹,当个符号就行.

Question

PI*[(a+b) /2]²-PI(a/2)²-PI(b/2)²,怎么计算,越详细越好.
PI是匹,当个符号就行.

Answer 1

π[(a+b) /2]²-π(a/2)²-π(b/2)^2
=π[(a+b)^2/4-a^2/4-b^2/4]
=(π/4)[a^2+2ab+b^2-a^2-b^2]
=πab/2.