10-4 Perimeter and Area in the Coordinate Plane Warm Up Lesson Presentation Lesson Quiz Holt McDougal Geometry Holt Geometry

Warm Up Use the slope formula to determine the slope of each line. 1. 2. 3. Simplify

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

Remember!

Example 1: Finding Perimeter and Area in the Coordinate Plane Draw and classify the polygon with vertices E(–1, –1), F(2, –2), G(–1, –4), and H(–4, –3). Find the perimeter and area of the polygon. Step 1 Draw the polygon.

Example 1 Continued Step 2 EFGH appears to be a parallelogram. To verify this, use slopes to show that opposite sides are parallel.

Example 1 Continued slope of EF = slope of GH = slope of FG = The opposite sides are parallel, so EFGH is a parallelogram. slope of HE =

Example 1 Continued Step 3 Since EFGH is a parallelogram, EF = GH, and FG = HE. Use the Distance Formula to find each side length. perimeter of EFGH:

Example 1 Continued To find the area of EFGH, draw a line to divide EFGH into two triangles. The base and height of each triangle is 3. The area of each triangle is The area of EFGH is 2(4.5) = 9 units2.

Example 2: 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.

Example 2 Continued Area of triangles: The area of the polygon is 48 – 9 – 3 – 9 – 3 = 24 units2.