Answer:
Part A) The approximate perimeter of the concrete region is [tex]P=64.66\ yd[/tex]
Par B) The exact area of the concrete region is [tex]A=(8\pi+162.4)\ yd^{2}[/tex]
Step-by-step explanation:
Part A) What is the approximate perimeter of the concrete region?
we know that
The perimeter of the composite figure is equal to
[tex]P=\pi r+2(15.2)+ 11.5+10.2[/tex]
The radius of semicircle is
[tex]r=8/2=4\ yd[/tex]
substitute
[tex]P=(3.14)(4)+2(15.2)+ 11.5+10.2=64.66\ yd[/tex]
Part B) What is the exact area of the concrete region?
we know that
The area of the composite figure is equal to the area of semicircle plus the area of rectangle plus the area of triangle
so
[tex]A=\frac{1}{2} \pi r^{2} +(15.2)(8)+\frac{1}{2}(10.2)(8)[/tex]
The radius of semicircle is
[tex]r=8/2=4\ yd[/tex]
[tex]A=\frac{1}{2} \pi (4)^{2} +(15.2)(8)+\frac{1}{2}(10.2)(8)[/tex]
[tex]A=8\pi+121.6+40.8[/tex]
[tex]A=(8\pi+162.4)\ yd^{2}[/tex]
