Answer:
[tex]A=9.5\ ft^2[/tex]
Step-by-step explanation:
we know that
The area of the shaded region is equal to the area of triangle plus the area of semicircle
so
[tex]A=\frac{1}{2}bh+\frac{1}{2}\pi r^{2}[/tex]
we have
[tex]b=4\ ft[/tex]
Find the height of the right triangle applying the Pythagorean Theorem
[tex]5^2=h^2+4^2[/tex]
[tex]h^2=9\\h=3\ ft[/tex]
The radius of the semicircle is half the height of triangle
[tex]r=3/2=1.5\ ft[/tex]
substitute in the formula
[tex]A=\frac{1}{2}(4)(3)+\frac{1}{2}(3.14)(1.5)^{2}[/tex]
[tex]A=6+3.5=9.5\ ft^2[/tex]
