Respuesta:
Area coloreada = (area rectángulo) - (area 3 trinagulo) = A - B
Area rectángulo = (9x -1)(2x + 4) = 18x^2 + 34x - 4 = A
Triangulo
izquierda = (2x + 2)(3x)/2 = 3x^2 + 3x
direita superior = (6x)(x + 3)/2 = 3x^2 + 9x
inferior = (6x - 1)(X + 1)/2 = 1/2(6x^2 + 5x - 1)
Suma area triangulos:
3x^2 + 3x + 3x^2 + 9x + 1/2(6x^2 + 5x - 1)
= 6x^2 + 12x + 3x^2 + 1/2(5x - 1)
= 9x^2 + 12x + 1/2(5x - 1) = B
A - B = (18x^2 + 34x - 4) - [9x^2 + 12x + 1/2(5x - 1)
= 18x^2 + 34x - 4 - 9x^2 - 12x - 1/2(5x - 1)
= 9x^2 + 22x - 4 - 1/2(5x - 1)
= 9x^2 + 22x - 4 - 5/2x + 1/2
= 9x^2 + (22 - 5/2)x - 7/2
= 9x^2 + (39/2)x - 7/2
AREA SOMBREADA = 9x^2 + (39/2)x - 7/2
Explicación paso a paso:
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