1. Objective
Find the perimeters and areas of figures in a coordinate plane.

2. Check It Out! Example 2
Draw and classify the polygon with vertices H(–3, 4), J(2, 6), K(2, 1), and L(–3, –1). Find the perimeter and area of the polygon.
Step 1 Draw the polygon.

3. Check It Out! Example 2 Continued
Step 2 HJKL appears to be a parallelogram. To verify this, use slopes to show that opposite sides are parallel.

4. Check It Out! Example 2 Continued
are vertical lines.
The opposite sides are parallel, so HJKL is a parallelogram.

5. Check It Out! Example 2 Continued
Step 3 Since HJKL is a parallelogram, HJ = KL, and JK = LH.
Use the Distance Formula to find each side length.
perimeter of EFGH:

6. Check It Out! Example 2 Continued
To find the area of HJKL, draw a line to divide HJKL into two triangles. The base and height of each triangle is 3. The area of each triangle is
The area of HJKL is 2(12.5) = 25 units2.

7. Example 3: Finding Areas in the Coordinate Plane by Subtracting
Find the area of the polygon with vertices A(–4, 1), B(2, 4), C(4, 1), and D(–2, –2).
Draw the polygon and close it in a rectangle.
Area of rectangle:
A = bh = 8(6)= 48 units2.

8. Example 3 Continued
Area of triangles:
The area of the polygon is 48 – 9 – 3 – 9 – 3 = 24 units2.

9. Check It Out! Example 3
Find the area of the polygon with vertices
K(–2, 4), L(6, –2), M(4, –4), and N(–6, –2).
Draw the polygon and close it in a rectangle.
Area of rectangle:
A = bh = 12(8)= 96 units2.

10. Check It Out! Example 3 Continued
Area of triangles: a b d c
The area of the polygon is 96 – 12 – 24 – 2 – 10 = 48 units2.