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»GEOMETRIE SINTETICA IN PLAN

Data publicarii: 27 Martie, 2011

ARII

Aria suprafetei triunghiului:

$\mathcal{A}=$ \mathcal{A}= $\frac{{a}\cdot{{h}_{a}}}{2}=$ \frac{{a}\cdot{{h}_{a}}}{2}= $\frac{b\cdot{h_b}}{2}=$ \frac{b\cdot{h_b}}{2}= $\frac{{c}\cdot{{h}_{c}}}{2};$ \frac{{c}\cdot{{h}_{c}}}{2};
$\mathcal{A}=$ \mathcal{A}= $\frac{{ab}\cdot{sinC}}{2}=$ \frac{{ab}\cdot{sinC}}{2}= $\frac{{bc}\cdot{sinA}}{2}=$ \frac{{bc}\cdot{sinA}}{2}= $\frac{{ca}\cdot{sinB}}{2};$ \frac{{ca}\cdot{sinB}}{2};
$\mathcal{A}=\frac{{a^2}\sin{B}\sin{C}}{2\sin{A}}=\frac{{b^2}\sin{C}\sin{A}}{2\sin{B}}=\frac{{c^2}\sin{A}\sin{B}}{2\sin{C}};$ \mathcal{A}=\frac{{a^2}\sin{B}\sin{C}}{2\sin{A}}=\frac{{b^2}\sin{C}\sin{A}}{2\sin{B}}=\frac{{c^2}\sin{A}\sin{B}}{2\sin{C}};
$\mathcal{A}=\sqrt{p(p-a)(p-b)(p-c)},\;unde\; p = \frac{a+ b +c}{2}.$ \mathcal{A}=\sqrt{p(p-a)(p-b)(p-c)},\;unde\; p = \frac{a+ b +c}{2}.

(formula lui Héron)

Aria suprafetei patratului:

A = l².

Aria suprafetei dreptunghiului:

A = L·l.

Aria suprafetei paralelogramului:

A = b·h.

Aria suprafetei rombului:

A = D·d.

Aria suprafetei trapezului:

$\mathcal{A}=\frac{{(\mathcal{B}+b)}\cdot{i}}{2}.$ \mathcal{A}=\frac{{(\mathcal{B}+b)}\cdot{i}}{2}.

Aria suprafetei cercului:

${\mathcal{A}}_{cerc}=\pi{R}^{2};$ {\mathcal{A}}_{cerc}=\pi{R}^{2};

Aria suprafetei sectorului circular:

${\mathcal{A}}_{sect}=\frac{{\pi}{R^2}{n^\circ}}{{360}^{\circ}}=\frac{{\mathit{l}_{arc}}\cdot{R}}{2}.$ {\mathcal{A}}_{sect}=\frac{{\pi}{R^2}{n^\circ}}{{360}^{\circ}}=\frac{{\mathit{l}_{arc}}\cdot{R}}{2}.