The proof that the area of the trapezium is 2x² + x -351 = 0 can be seen in the image attached below.
What is a trapezium?
A trapezium is a quadrilateral that has a pair of opposite parallel sides.
From the given diagram:
The area of the trapezium can be computed as;
[tex]\mathbf{= \dfrac{1}{2} \times (sum \ of \ the \ parallel \ sides) \times height }[/tex]
[tex]\mathbf{351= \dfrac{1}{2} \times (x-4 + x +5) \times 2x }[/tex]
[tex]\mathbf{351= \dfrac{1}{2} \times (2x+1) \times 2x }[/tex]
[tex]\mathbf{351= (2x+1) \times x }[/tex]
351 = 2x² + x
2x² +x - 351 = 0 : Proved
Learn more about the area of trapezium here:
https://brainly.com/question/16904048
