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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. Objective. Find the perimeters and areas of figures in a coordinate plane. In Lesson 9-3, you estimated the area of irregular shapes by drawing composite figures that approximated the irregular

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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. Objective Find the perimeters and areas of figures in a coordinate plane. In Lesson 9-3, you estimated the area of irregular shapes by drawing composite figures that approximated the irregular shapes and by using area formulas. Another method of estimating area is to use a grid and count the squares on the grid.

  3. 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.

  4. Remember!

  5. 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.

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

  7. 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.

  8. 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:

  9. 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.

  10. 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.

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

  12. 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.

  13. 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.

  14. IN-Class Assignment Worksheet Reteach 9-4

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