## Quick Reference

Using the properties of angles made when one line cuts a pair of parallel lines, it is proved, as illustrated on the left, that the angles of a triangle *ABC* add up to 180∘. By considering separate areas, illustrated on the right, it can be shown that the area of the triangle is half that of the rectangle shown, and so the area of a triangle is ‘half base times height’.

If now *A*, *B* and *C* denote the angles of the triangle, and *a*, *b* and *c* the lengths of the sides opposite them, the following results hold: *bc* sin *A*.*R* is the radius of the circumcircle.*a*^{2}=*b*^{2}+*c*^{2}−2*bc* cos *A*, or, in another form,*s*=½(*a*+*b*+*c*). Then the area of the triangle equals

*bc* sin *A*.

*R* is the radius of the circumcircle.

*a*^{2}=*b*^{2}+*c*^{2}−2*bc* cos *A*, or, in another form,

*s*=½(*a*+*b*+*c*). Then the area of the triangle equals

*Subjects:*
Mathematics.