- 收集三角形面积公式设a,b,c;ma,mb,mc;ha,hb,h
- 设a,b,c;ma,mb,mc;ha,hb,hc;ra,rb,rc分别表示△AB的三边长,中线,高和旁切圆半径，s,R,r分别表示△ABC的半周长，外接与内切半径，A,B,C分别表示△ABC的三内角。请给出三角形面积的表示式。
- 设a,b,c;ma,mb,mc;ha,hb,hc;ra,rb,rc分别表示△AB的三边长,中线,高和旁切圆半径，s,R,r分别表示△ABC的半周长，外接与内切半径，A,B,C分别表示△ABC的三内角。请给出三角形面积的表示式。
设三角形面积为△，根据三角形诸元素之间的恒等变换关系，列出下列21种三角形面积公式。仅供参考。
(1),△=sr;
(2),△=(s-a)*ra=(s-b)*rb=(s-c)*rc;
(3),△=√(r*ra*rb*rc);
(4),△=ra*rb*rc/√(rb*rc+rc*ra+ra*rb);
(5),△=s^2*tan(A/2)*tan(B/2)*tan(C/2);
(6),△=s*(s-a)*tan(A/2)=s*(s-b)*tan(B/2)=s*(s-c)*tan(C/2);
(7),△=abc/(4R);
(8),△=bc*sinA/2=ca*sinB/2=ab*sinC/2;
(9),△=abc*cos(A/2)*cos(B/2)*cos(C/2)/s;
(10),△=2R^2*sinA*sinB*sinC;
(11),△=a^2*sinB*sinC/sinA= b^2*sinC*sinA/sinB= c^2*sinA*sinB/sinC;
(12),△=(a^2/sinA+b^2/sinB+c^2/sinC)*sin(A/2)*sin(B/2)*sin(C/2);
(13),△=[(b^2+c^2)*sin(2A)+(c^2+a^2)*sin(2B)+(a^2+b^2)*sin(2C)]/12;
(14),△=2s^2*sinA*sinB*sinC/(sinA+sinB+sinC)^2;
(15),△=√{(a^4+b^4+c^4)/[8(cotA)^2+8(cotB)^2+8(cotC)^2+8]};
(16),△=a^2/[2(cotB+cotC)]=b^2/[2(cotC+cotA)]=c^2/[2(cotA+cotB)];
(17),△=[b^2*sin(2C)+c^2*sin(2B)]/4=[c^2*sin(2A)+a^2*sin(2C)]/4
=[a^2*sin(2B)+b^2*sin(2A)]/4;
(18),△=√[(ma+mb+mc)*(mb+mc-ma)*(mc+ma-mb)*(ma+mb-mc)]/3;
(19),△=1/
√[(1/ha+1/hb+1/hc)*(1/hb+1/hc-1/ha)*(1/hc+1/ha-1/hb)*(1/ha+1/hb-1/hc)];
(20),△=a*ha/2=b*hb/2=c*hc/2;
(21),△=(ha*sinA+hb*sinB+hc*sinC)^2/(18*sinA*sinB*sinC).