Answer
40.77
Work Step by Step
Step 1. Draw a line to divide the area into two triangles as shown in the figure (not to scale).
Step 2. For the top triangle, use the Law of cosines to obtain the length $x^2=5^2+6^2-2\times5\times6cos100^{\circ}\approx71.42$ and $x\approx8.45$
Step 3. Use the Heron's Formula for the top triangle to get $s=\frac{5+6+8.45}{2}=9.725$ and the area is given by
$A1=\sqrt {9.725(9.725-5)(9.725-6)(9.725-8.45)}\approx14.77$
Step 4. Use the Heron's Formula for the top triangle to get $s=\frac{7+8+8.45}{2}=11.725$ and the area is given by $A2=\sqrt {11.725(11.725-7)(11.725-8)(11.725-8.45)}\approx26.00$
Step 5. The total area is $A1+A2=40.77$
