Solving Area of shapes

Question

I keep getting the same answer to this question:

I've attached my working out as well.

Answer 1

It is easier to calculate the area with coordinates. The coordinates of the four vertexes are

$$A(0,0),\>\>\>\>B(72,0),\>\>\>C(72+81\cos60,81\sin60),\>\>\>D(-63\cos80, 63\sin80)$$

Use the coordinate area formula for the triangle ABC to calculate its area,

$$S_{ABC} = \frac12| A_x(B_y-C_y) + B_x(C_y-A_y) + C_x(A_y-B_y)|=2525.3$$

Similarly, the area of the triangle ACD is

$$S_{ACD} = \frac12| A_x(C_y-D_y) + C_x(D_y-A_y) + D_x(A_y-C_y)|=3873.6$$

Thus, the total area is

$$S_{ABCD} = S_{ABC} + S_{ACD} = 2525.3+ 3873.6=6398.9$$