Triangle ACF is right
Let
A = (0, 4) B = (7,0) E = (0,2) F(3,0) C = (0,0)
The line joining AF has a slope of [ -4/3 ]
And the equation of this line is y = (-4/3)x + 4 (1)
The line joining BE has a slope of [ -2/7]
And the equation of this line is y = (-2/7) x +2 ( 2)
We can find the coordinates of D by equating (1) and (2)
(-4/3)x + 4 = (-2/7)x + 2
4 - 2 = ( 4/3 - 2/7)x
2 = ( 22/21) x
(2)(21)/22 = x = 21/11
And y = (-4/3) (21/11) + 4 = 16/11
So....the area of triangle ACF = (1/2) (4) (3) = 6
And the area of triangle DFB = (1/2) (16/11) (4) = 32/11
And the area of triangle ACB = (1/2) (4) (7) = 14
So....the area of triangle ADB =
14 - 32/11 - 6 =
8 -32/11
[88 - 32 ] /11 =
56 / 11 units^2