Question

Write an expression to represent the area of the figure.

a)5x^3 + 24.5x^2 + 70.5x + 56
b)10x^3 + 49x^2 + 141x + 56
c)15x^2 + 6x - 48
d)7.5x^2 + 3x - 24

Answer 1

`Area\ of\ trapezoid:A=(b_1+b_2)/(2)\cdot h\\\\b_1;\ b_2-base;\ h-height\\-------------------\\b_1=x+7;\ b_2=2x-1;\ h=5x-8\\\\subtitute:\\\\A=((x+7)+(2x-1))/(2)\cdot(5x-8)=(3x+6)/(2)\cdot(5x-8)\\\\=((3x+6)(5x-8))/(2)=((3x)(5x)+(3x)(-8)+(6)(5x)+(6)(-8))/(2)\\\\=(15x^2-24x+30x-48)/(2)=(15x^2+6x-48)/(2)\\\\=(15x^2)/(2)+(6x)/(2)-(48)/(2)=\boxed{7.5x^2+3x-24}\leftarrow\boxed{\boxed{d)}}`