Respuesta :

Answer:

A = 5x² + 6x + 1

Step-by-step explanation:

The area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (a + b)

where h is the height and a, b the parallel bases, thus

A = [tex]\frac{1}{2}[/tex] (x + 1)(6x - 5 + 4x + 7)

   = [tex]\frac{1}{2}[/tex] (10x + 2)(x + 1)

   = (5x + 1)(x + 1) ← distribute using FOIL

   = 5x² + 6x + 1

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The expression for the area of the trapezoid is required.

The required equation is [tex]A=5x^2+6x+1[/tex]

The bases are

[tex]a=6x-5[/tex]

[tex]b=4x+7[/tex]

h = Height = [tex]x+1[/tex]

The area of the trapezoid is

[tex]A=\dfrac{(a+b)h}{2}\\\Rightarrow A=\dfrac{(6x-5+4x+7)(x+1)}{2}\\\Rightarrow A=\dfrac{(10x+2)(x+1)}{2}\\\Rightarrow A=\dfrac{10x^2+10x+2x+2}{2}\\\Rightarrow A=\dfrac{10x^2+12x+2}{2}\\\Rightarrow A=5x^2+6x+1[/tex]

The required equation is [tex]A=5x^2+6x+1[/tex]

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