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

Warm Up Use the slope formula to determine the slope of each line. 1. 2. 3. Simplify. Perimeter and Area in the Coordinate Plane. 9-4. Holt Geometry. Example 1A: Estimating Areas of Irregular Shapes in the Coordinate Plane. Estimate the area of the irregular shape. Example 1A Continued.

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

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

  2. Perimeter and Area in the Coordinate Plane 9-4 Holt Geometry

  3. Example 1A: Estimating Areas of Irregular Shapes in the Coordinate Plane Estimate the area of the irregular shape.

  4. Example 1A Continued Method 1: Draw a composite figure that approximates the irregular shape and find the area of the composite figure. The area is approximately 4 + 5.5 + 2 + 3 + 3 + 4 + 1.5 + 1 + 6 = 30 units2.

  5. Method 2: Count the number of squares inside the figure, estimating half squares. Use a  for a whole square and a for a half square. Example 1A Continued There are approximately 24 whole squares and 14 half squares, so the area is about

  6. Check It Out! Example 1 Estimate the area of the irregular shape. There are approximately 33 whole squares and 9 half squares, so the area is about 38 units2.

  7. Example 2: 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.

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

  9. slope of EF = slope of FG = slope of GH = slope of HE = Example 2 Continued The opposite sides are parallel, so EFGH is a parallelogram.

  10. Example 2 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:

  11. Example 2 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.

  12. 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.

  13. 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.

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

  15. P619 #2-8 evens

  16. Kite; P = 4 + 2√10 units; A = 6 units2 Lesson Quiz: Part I 1. Estimate the area of the irregular shape. 25.5 units2 2. Draw and classify the polygon with vertices L(–2, 1), M(–2, 3), N(0, 3), and P(1, 0). Find the perimeter and area of the polygon.

  17. Lesson Quiz: Part II 3. Find the area of the polygon with vertices S(–1, –1), T(–2, 1), V(3, 2), and W(2, –2). A = 12 units2 4. Show that the two composite figures cover the same area. For both figures, A = 3 + 1 + 2 = 6 units2.

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