To calculate the perimeter of the rectangle KLMN, we can use the coordinates of the vertices given in the diagram:

• $K(1, 10)$
• $L(9, 10)$
• $M(9, 7)$
• $N(1, 7)$

Step 1: Calculate the Lengths of the Sides

• Length of KL (horizontal side): $\text{Distance between } K(1, 10) \text{ and } L(9, 10) = |9 - 1| = 8 \text{ units}$
• Length of KN (vertical side): $\text{Distance between } K(1, 10) \text{ and } N(1, 7) = |10 - 7| = 3 \text{ units}$

Since this is a rectangle, the opposite sides are equal. Thus:

• $LM = KN = 3 \text{ units}$
• $MN = KL = 8 \text{ units}$

Step 2: Calculate the Perimeter

The perimeter $P$ of a rectangle is given by the formula: $P = 2(\text{Length} + \text{Width})$ Substituting the values: $P = 2(8 + 3) = 2 \times 11 = 22 \text{ units}$

Thus, the perimeter of rectangle KLMN is 22 units.

Would you like further clarification or more details? Here are some related questions for practice:

1. How would the perimeter change if one of the side lengths doubled?
2. Can you calculate the area of rectangle KLMN based on the given dimensions?
3. How do you find the length of the diagonal in a rectangle?
4. What are some real-life applications of calculating perimeters?
5. How would the perimeter change if the rectangle was rotated?

Tip: Always double-check coordinates when calculating side lengths, especially if the diagram isn't drawn to scale.