Answer :
The perimeter of the figure is 50.56 cm.
Solution:
Radius of the quarter of a circle = 8 cm
Perimeter of the quarter circle = [tex]\frac{1}{4} 2\pi r[/tex]
[tex]$=\frac{1}{4} \times 2 \times 3.14 \times 8[/tex]
= 12.56 cm
In figure, one side of the quarter circle is merged with rectangle, so remove one radius from the perimeter of the quarter circle.
Perimeter of the given quarter circle = 12.56 cm – one radius
= 12.56 cm – 8 cm
= 4.56 cm
Perimeter of the rectangle given = (17 – 8) cm + 10 cm + 17 cm + 10 cm
= 9 cm + 10 cm + 17 cm + 10 cm
= 46 cm
Perimeter of the given figure = 4.56 cm + 46 cm
= 50.56 cm
Hence the perimeter of the figure is 50.56 cm.