There are three parts to this trapezoid, a rectangle in the middle, and two
right triangles on each end.

On the left, we have a special right triangle, a 6-8-10 right triangle,
whose sides are twice a 3-4-5 right triangle.

To calculate the longer leg 8, if you need to,  

So the area of the triangle on the left is



The area of the rectangle in the middle is



The area of the right triangle on the right:



Adding the 3 parts:



Edwin