Question

examineaza desenul.
ABCD este dreptunghi si AB =0,6BC
a)calculati raza cerclui din care provine semicercul daca x=14,4cm
b)aflati perimetru figurii
c)aflati aria figurii

Answer 1

Răspuns:

Explicație pas cu pas:

$\displaystyle AB=0,6\times BC=\frac{6}{10} \times BC = \frac{3}{5} \times BC$

X=AB si X=14,4 ⇒     14,4 = AB

$\displaystyle 14,4 = \frac{3}{5} \times BC\\\\\frac{144}{10} = \frac{3}{5} \times BC$

$\displaystyle BC=\frac{\not5\times144}{3\times \not10} =\frac{\not144}{\not3\times 2} =\frac{48}{2} =24$

BC diametru deci raza va fi jumatate din BC

$\displaystyle Raza = \frac{BC}{2} =\frac{24}{2} =12$

$\displaystyle L_{cerc} =2\pi R\\L_{cerc} =12\times2\pi =24\pi$

$\displaystyle P_{semicerc} =\frac{L_{cerc} }{2} =\frac{24\pi }{2} =12\pi$

$\displaystyle P_{ABCD} =2AB+2BC=2(AB+BC)=2(0,6BC+BC)=2\times1,6 BC=3,2\times BC=3,2\times 24=76,8$

$\displaystyle P_{figurii} =P_{semicerc} +P_{ABCD} =12\pi +76,8=12(6,4+\pi )$

$\displaystyle A_{cerc} =\pi R^{2} =\pi 12^{2} =144\pi \\A_{semicerc} =A_{cerc} :2=144\pi :2=72\pi \\A_{ABCD} = AB\times BC=14,4 \times 24=345,6\\A_{figura} =A_{semicerc} +A_{ABCD} =72\pi +345,6=72(4,8 +\pi )$