Show that Trapezium

Question

The height of the trapezium is (x-1)

The length of the trapezium is (3x-4)

the length at the top of the trapezium is (x+6)

The area of the trapezium is 119cm^2

Show that 2x^2-x-120=0

Answer 1

A trapezium is alternatively known as a trapezoid, in the United States, a quadrilateral with at least one parallel pair of sides

The formula for Area is A=(a+b)h/2 or the average of the two parallel sides, a and b, times the distance between them, h, or height.

So, in this given example, with a=x+6, b=3x-4 and h=x-1:

The area 119 = A=(x+6 + 3x - 4)(x-1)/2 = (4x+2)(x-1)/2 = (2x+1)(x-1) = 2x² -x -1 = 119

subtract 119 from both sides to get:

or 2x² -x -120 = 0