Question

In triunghiul ABC construim inaltimile AD,D apartineBC,BE,E apartineAC si CF,F apartineAB.Calculati aria triunghiului ABC in urmatoarele cazuri: a) AB=12 cm si CF=13 cm;b) BC=23 cm si AD=10 cm: c) AC=16 CM SI BE=8,5 cm.

Answer 1

[tex]\Delta ABC: \\ D\in BC; \ AD \bot BC;\\ E \in AC; \ BE \bot AC; \\ F \in AB ; \ FC \bot AB;\\\boxed{\bold{A_{\Delta}=\frac{a \cdot h}{2}}} \\ \bold{a)} \ AB=a=12 \ cm; \ CF=h=13 \ cm; \\ \Rightarrow A_{\Delta}=\frac{12 \ cm \cdot \ 13 \ cm}{2}=6 \ cm \cdot 13 \ cm=\boxed{\bold{78 \ cm^2}}; \\ \\ \bold{b)} \ BC=a=23 \ cm; \ AD=h=10 \ cm; \\ \Rightarrow A_{\Delta}=\frac{23 \ cm \cdot 10 \ cm}{2}=23 \ cm \cdot 5 \ cm=\boxed{\bold{115 \ cm^2}};[/tex]

$\bold{c)} \ AC=a=16 \ cm; \ BE=h=8,5 \ cm; \\ \Rightarrow A_{\Delta}=\frac{16 \ cm \cdot 8,5 \ cm}{2}=8\ cm \cdot 8,5 \ cm=\boxed{\bold{68 \ cm^2}};$