Perimeter andand Area in Perimeter in 10 4

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Perimeter andand Area in Perimeter in 10 -4 the Coordinate Plane Warm Up Lesson

Perimeter andand Area in Perimeter in 10 -4 the Coordinate Plane Warm Up Lesson Presentation Lesson Quiz Holt. Mc. Dougal Geometry Holt

10 -4 Perimeter and Area in the Coordinate Plane Warm Up Use the slope

10 -4 Perimeter and Area in the Coordinate Plane Warm Up Use the slope formula to determine the slope of each line. 1. 2. 3. Simplify Holt Mc. Dougal Geometry

10 -4 Perimeter and Area in the Coordinate Plane Objective Find the perimeters and

10 -4 Perimeter and Area in the Coordinate Plane Objective Find the perimeters and areas of figures in a coordinate plane. Holt Mc. Dougal Geometry

10 -4 Perimeter and Area in the Coordinate Plane Remember! Holt Mc. Dougal Geometry

10 -4 Perimeter and Area in the Coordinate Plane Remember! Holt Mc. Dougal Geometry

10 -4 Perimeter and Area in the Coordinate Plane Example 1: Finding Perimeter and

10 -4 Perimeter and Area in the Coordinate Plane 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. Holt Mc. Dougal Geometry

10 -4 Perimeter and Area in the Coordinate Plane Example 1 Continued Step 2

10 -4 Perimeter and Area in the Coordinate Plane Example 1 Continued Step 2 EFGH appears to be a parallelogram. To verify this, use slopes to show that opposite sides are parallel. Holt Mc. Dougal Geometry

10 -4 Perimeter and Area in the Coordinate Plane Example 1 Continued slope of

10 -4 Perimeter and Area in the Coordinate Plane Example 1 Continued slope of EF = slope of GH = slope of FG = slope of HE = Holt Mc. Dougal Geometry The opposite sides are parallel, so EFGH is a parallelogram.

10 -4 Perimeter and Area in the Coordinate Plane Example 1 Continued Step 3

10 -4 Perimeter and Area in the Coordinate Plane 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: Holt Mc. Dougal Geometry

10 -4 Perimeter and Area in the Coordinate Plane Example 1 Continued To find

10 -4 Perimeter and Area in the Coordinate Plane 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 units 2. Holt Mc. Dougal Geometry

10 -4 Perimeter and Area in the Coordinate Plane Example 2: Finding Areas in

10 -4 Perimeter and Area in the Coordinate Plane 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 units 2. Holt Mc. Dougal Geometry

10 -4 Perimeter and Area in the Coordinate Plane Example 2 Continued Area of

10 -4 Perimeter and Area in the Coordinate Plane Example 2 Continued Area of triangles: The area of the polygon is 48 – 9 – 3 = 24 units 2. Holt Mc. Dougal Geometry