Quadrilateral ABCD Area??

Question

The lines 2x+y=6 and x+y=10 together with the x-axis and y-axis are drawn pn a coordinate grid to form quadrilateral ABCD. What is the area of quadrilateral ABCD

Answer 1

Hi Luna R.,

If you plot the graph of 2x+y=6, the x-intercept is (3, 0), and the y-intercept is ((0, 6). This forms a triangle in quadrant I, lets call this triangle M. Then plot x+y = 10, the x-intercept is (10, 0), and the y-intercept is (0, 10). This forms another larger triangle in quadrant I, lets call this triangle N. The quadrilateral formed is the difference of these two triangles. Therefore if you find the area of triangle M and triangle N, you can subtract the area of triangle M from the area of triangle N, and this will be the area of the quadrilateral.

Area of triangle M = (1/2)*(3)*(6) = 9

Area of triangle N = (1/2)*(10)*(10) = 50

Area of the quadrilateral:

N - M = 50 - 9 = 41

I hope this helps, Joe.