Answer:
[tex]80\text{ mm}+\frac{15\pi}{2}\text{ mm} \approx 103.56\text{ mm}[/tex]
Step-by-step explanation:
This question asks us to find the perimeter of the given figure, a rectangle and a quadrant (a quarter of a circle).
First, we will find the perimeter of the rectangle, keeping in mind that one of the sides isn't in the perimeter.
P = 25 mm + 25 mm + 15 mm = 65 mm
Now, we will find the perimeter of the quadrant. Keep in mind that one side is attached to our rectangle. The radius of this quadrant is 15 mm, which is equal to the side on the ground. This means we will add 15 mm to the perimeter of a quarter circle, also known as the circumference.
[tex]\displaystyle P = 15 mm +\frac{2\pi r}{4} = 15\text{ mm}+\frac{15\pi}{2}\text{ mm}[/tex]
Lastly, we will add this all together.
[tex]\displaystyle 65\text{ mm}+15\text{ mm}+\frac{15\pi}{2}\text{ mm}=80\text{ mm}+\frac{15\pi}{2}\text{ mm} \approx 103.56\text{ mm}[/tex]