The diagram shows a trapezoidal area with the following side lengths: a vertical side of 6 units, a horizontal side of 4 units, and another vertical side of 3 units. The last side is slanted, which we can calculate using the Pythagorean theorem.

Step 1: Calculate the length of the slanted side

This slanted side forms a right triangle with the horizontal distance (4 - 3 = 1 unit) and the vertical distance (6 - 3 = 3 units).

Using the Pythagorean theorem: $\text{Slanted side} = \sqrt{(1^2 + 3^2)} = \sqrt{(1 + 9)} = \sqrt{10} \approx 3.16 \text{ units}$

Step 2: Calculate the perimeter

Now, sum the lengths of all four sides: $\text{Perimeter} = 6 + 4 + 3 + 3.16 \approx 16.16 \text{ units}$

Thus, the perimeter of the area to be fenced is approximately 16.16 units.

Would you like further details or explanations?

Related Questions:

1. How would you calculate the area of the trapezoid?
2. What is the importance of the Pythagorean theorem in geometry?
3. Can you determine the type of trapezoid based on its sides?
4. How would the perimeter change if the slanted side were longer?
5. How does perimeter differ from area?

Tip:

In geometry, always double-check your right triangles when calculating slanted or diagonal sides, as they often involve the Pythagorean theorem.