Question

A trapezoid is formed by lines with the following equations.

2x+y= 16
x= 4
x= 0
y= 0

Find the area of the trapezoid.

Answer 1

OABC is the trapezoid. Area of trapezoid =
1/2 * (sum of the parallel sides) * distance between the parallel sides.
Area = 1/2 * (OC + AB) * OA
OA = 4 because point A is (4,0) and point O is (0,0)
Area = 1/2 * (OC + AB) * OA = 1/2 * (OC + AB) * 4 = 2 * (OC + AB)

To find OC, we need the coordinates of point C. Point C is the y-intercept of the line 2x+y=16. What is the y-intercept?
Point B is the intersection of the line x = 4 and 2x+y=16. Find point B.