In triangle ABC, side AB = 13 cm, BC = 14 cm, AC = 15 cm. Find the area of ​​triangle ABC:
1) by first calculating the height to the AC side;

Відповідь:

A(∆ABC)=84cm²

h=11,2cm

Розв'язання:

Формула Герона.

A(∆ABC)=√(p(p-AB)(p-BC)(p-AC));

p=(AB+BC+AC)/2=(13+14+15)/242/2=21cm

A(∆ABC)=√(21(21-13)(21-14)(21-15))=

=√(21*8*7*6)=√(7*3*4*2*7*2*3)=7*3*4=

=84cm²

A(∆ABC)=½*AC*h;

h=2*A(∆ABC)/AC=2*84/15=168/15=

=11,2cm