Geometria

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$\small\text{Area parte colorata:}$

$\small A= (4+x)(x+1+x+2)-(x(x+1)+3x)$

$\small A= (4+x)(2x+3)-(x^2+x+3x)$

$\small A= 8x+12+2x^2+3x-(x^2+4x)$

$\small A= 11x+12+2x^2-x^2-4x$

$\small A= 7x+12+x^2$

$\small A= x^2+7x+12\; \Longrightarrow\; = (x+4)(x+3).$

$\small\text{Perimetro del rettangolo:}$

$\small 2p= 2(4+x)+(x+1+x+2)+3+(x+1+x+2)-3$

$\small 2p= 8+2x+2x+3+3+2x\cancel{+3}\cancel{-3}$

$\small 2p= 14+6x$

$\small 2p= 6x+14 \;\Longrightarrow \;= 2(3x+7).$

perimetro 2p = 2(4+x)+2(2x+3) = 8+2x+4x+6 = 6x+14 = 2(3x+7)

area colorata Ac= (4+x)(2x+3)-x^2-x-3x

Ac = 8x+12+2x^2+3x-x^2-3x = x^2+7x+12 = (x+3)(x+4)

Lati del rettangolo grande:

base = (x + 2) + (x + 1);

altezza = 4 + x;

base = x + x + 2 + 1 = 2x + 3;

Perimetro = 2 * (b + h) = 2 * (2x + 3 + 4 + x) ;

Perimetro = 2 * (3x + 7) = 6x + 14;

Area rettangolo = (2x + 3) * (4 + x);

Area rettangolo grande =

A = 8x + 2x^2 + 12 + 3x;

A = 2x^2 + 11 x + 12;

Area dei rettangolini bianchi: A1 + A2;

A1 = 3 x;

A2 = x * (x + 1) = x^2 + x;

A1 + A2 = 3x + x^2 + x = x^2 + 4x;

Area gialla = A - (A1 + A2);

Area gialla = 2x^2 + 11 x + 12 - (x^2 + 4x);

Area gialla = 2x^2 + 11 x + 12 - x^2 - 4x ;

Area gialla = x^2 + 7x + 12.

Ciao  @michele-09