Question

Find the area of the triangles with the given sides.

(a) 21 cm, 17 cm, 10 cm 

(b) 12 cm, 16 cm, 20 cm 

(c) 34 cm, 30 cm, 16 cm 

(d) 20 cm, 21 cm, 29 cm

Answer 1

(a) \(\sqrt{S(S-a)(S-b)(S-c)}\)

\(S=\frac{a+b+c}{2}=\frac{21+17+10}{2}=24\) cm²

\(\sqrt{24(24-21)(24-17)(24-10)}\)

 \(=\sqrt{24\times3\times7\times14}=84\) cm²

(b) \(\sqrt{24(24-12)(24-16)(24-20)}\)

\(S=\frac{12+16+20}{2}=24\)

= \(\sqrt{24\times12\times8\times4}=96\) cm²