A quadrilateral is formed by the four lines where y=5, x=8, y=2x-5, and y= -3. Find the area of the quadrilateral

Answer 1

Since the area is bounded by two parallel lines y=5 and y=-3, the area is a trapezoid, with a height of (5-(-3))=8.

We need to find the intersection of the line y=2x-5 with each of the parallel lines.
Setting 5=2x-5 => x=5
Setting -3=2x-5 => x=1
So the upper width is (8-5)=3
and the lower width is (8-1)=7
The area of the trapezoid is therefore
Area = (1/2)(3+7)*8
=40 units.