Answer:
\(37.55\ m\)
Step-by-step explanation:
we know that
The perimeter of the figure is equal to the perimeter of semicircle plus the perimeter of quarter circle plus two times the length of \(2\ m\) plus two times the length of \(5\ m\)
Find the perimeter of semicircle
we know that
The circumference of a semicircle is equal to
\(C=\frac{1}{2}\pi D\)
we have
\(D=10\ m\)
substitute
\(C=\frac{1}{2}\pi(10)=5 \pi\ m\)
Find the perimeter of a quarter of circle
we know that
The circumference of a quarter of circle is equal to
\(C=\frac{1}{4}\pi D\)
we have
\(D=10\ m\)
substitute
\(C=\frac{1}{4}\pi(10)=2.5 \pi\ m\)
Find the perimeter of the figure
\(5 \pi\ m+2.5 \pi\ m+2*2\ m+2*5\ m=7.5 \pi\ m+14\ m\)
\(7.5 \pi+14=37.55\ m\)
