check the picture below.
notice, the triangle has a base of 6, and an altitude (in red) of 5, whilst the semicircle has a radius of 3 units, so we can simply get the area of each, and sum them up.
[tex]\bf \stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(6)(5)}~~~~+~~~~\stackrel{\textit{area of the semicircle}}{\cfrac{\pi (3)^2}{2}}\implies 15+4.5\pi [/tex]
