Answer:
the perimeter of the figure is 66.56 cm.
Step-by-step explanation:
Hello.
Let's remember the perimeter of a rectangle and the perimeter of a circle
[tex]Perimeter\ of\ a\ rectangle=2(length)+2(width)\\Perimeter\ of\ a\ circle = 2\pi r \where\ r\ is\ the\ radius\ of\ the\ circle\\[/tex]
Now, the perimeter of a quarter circle is
[tex]\frac{Perimeter\ of\ a\ circle }{4}=\frac{2\pi r\ }{4} \\\\Perimeter\ of\ a\ quarter\ circle=\frac{\pi r}{2}\\[/tex]
Step 1
find the perimeter of the rectangle
[tex]Perimeter\ of\ a\ rectangle=2(length)+2(width)\\let\\length=17 cm\\width=10 cm\\\\Perimeter\ of\ the\ rectangle=2(17 cm )+2(10 cm)\\Perimeter\ of\ the\ rectangle= 34 cm +20 cm\\Perimeter\ of\ the\ rectangle=54 cm[/tex]
Step 2
find the perimeter of the quarter circle
[tex]Perimeter\ of\ a\ quarter\ circle=\frac{\pi r}{2} \\let\ r =8 cm\\\\\pi =3.1\\Perimeter\ of\ the\ quarter\ circle=\frac{3.14*8 cm}{2} =12.56 cm\\Perimeter\ of\ the\ quarter\ circle=12.56 cm[/tex]
step 3
find the total perimeter
the right side of the quarter of circle has a vertical line ,r=8 cm, that must be added to the perimeter, and the rectangle has a line in common with the quarter of circle, r= 8cm=, this length must be subtracted from the total perimeter
the total perimeter is
find the perimeter of the rectangle+perimeter of the quarter circle +r-r
total perimeter=54 cm +12.56 cm+8 cm -8 cm
total perimeter= 66.56 cm
have a great day
