The figure is a quarter circle, and you are asked to find its perimeter. The two legs of the right angle (5 yards each) form the radius of the quarter circle.

To find the perimeter of the quarter circle, we need to calculate the following components:

1. The curved part of the quarter circle (which is one-fourth of the full circumference of the circle).
2. The two straight edges that make up the radius of the quarter circle.

Step 1: Find the circumference of the full circle.

The formula for the circumference of a circle is:

$C = 2\pi r$

Since the radius $r$ is given as 5 yards, and $\pi = 3.14$:

$C = 2 \times 3.14 \times 5 = 31.4 \, \text{yards}$

Now, since this is a quarter circle, the length of the curved part is one-fourth of the circumference:

$\text{Curved part} = \frac{1}{4} \times 31.4 = 7.85 \, \text{yards}$

Step 2: Add the two radii.

The two straight edges are simply the radii of the quarter circle, so their total length is:

$\text{Total radii} = 5 + 5 = 10 \, \text{yards}$

Step 3: Calculate the total perimeter.

Now, we add the length of the curved part and the two radii:

$\text{Perimeter} = 7.85 + 10 = 17.85 \, \text{yards}$

Thus, the perimeter of the figure is 17.85 yards.

Would you like further details or have any questions?

Here are five related questions for further exploration:

1. What is the area of this quarter circle?
2. How would the perimeter change if the radius were doubled?
3. What is the perimeter of a semicircle with the same radius?
4. If the quarter circle were part of a larger shape, how would you calculate its total perimeter?
5. Can you derive the perimeter of a quarter circle using the general formula for circles?

Tip: When working with quarter or semicircles, always break down the problem into the straight edges and the curved part separately for better clarity.