Geometry Chapter 9 Extending Perimeter, Circumference, and Area

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1 Geometry Chapter 9 Extending Perimeter, Circumference, and Area Lesson 1 Developing Formulas for Triangles and Quadrilaterals Learning Target (LT-1) Solve problems involving the perimeter and area of triangles and special quadrilaterals. **Refer to the formula sheet for area formulas. Examples: 1. Find the area of the parallelogram. 2. Find the height of a rectangle in which b = 3 in. and A = (7x 2 + 8x 2) in 2 3. Find the perimeter of the rectangle in which A = (79.8x 2 42) cm Find the area of a trapezoid in which b 1 = 8in, b 2 = 5in, and h = 6.2in. 5. Find the base of the triangle in which A=(15x 2 )cm Find b 2 of the trapezoid, in which A = 231mm 2.

2 7. Find d 2 of a kite in which d 1 = 14in and A = 238in Find the area of the rhombus. 9. Find the area of the kite. 10. The tile design shown is a rectangle with a base of 4in and a height of 2in. Use the grid to find the perimeter and area of the leftmost shaded parallelogram. Lesson 2 Developing Formulas for Circles and Regular Polygons Learning Target (LT-2) Apply the formulas for the area and circumference of circles and the area and perimeter of regular polygons. Circle: Center of a Circle: π Center of a Regular Polygon Apothem: Central Angle of a Regular Polygon:

3 Examples: 1. Find the area of K in terms of π. 2. Find the radius of J if the circumference is (65x + 14)π m. 3. Find the circumference of M if the area is 25x 2 π ft A pizza-making kit contains three circular baking stones with diameters 24cm, 36cm, and 48cm. Find the area of each stone. Round to the nearest tenth. 5. Find the area of a regular heptagon with side length 2 ft. Round to the nearest tenth. 6. Find the area of a regular hexagon with apothem 6 cm. Round to the nearest tenth. Lesson 3 Composite Figures Learning Target (LT-3) Find the area of composite figures and estimate the areas of irregular shapes. Composite Figures:

4 Examples: In 1-4, find the shaded area. Round to the tenth A company receives an order for 65 pieces of fabric in the given shape. Each piece is to be dyed red. To dye 6in 2 of fabric, 2oz of dye is needed. How much dye is needed for the entire order? 6. Use a composite figure to estimate the shaded area. The grid has squares with a side length of 1ft.

5 Lesson 4 Perimeter and Area in the Coordinate Plane Learning Target (LT-4) Find the area and perimeter of figures in the 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. Examples: 1. Estimate the area of the irregular shape. 2. Estimate the area of the irregular shape. 3. Classify the polygon below. Find the perimeter and area of the polygon. 4. Classify the polygon below. Find the perimeter and area of the polygon.

6 5. Find the areas in the coordinate plane by subtracting. 6. Find the area in the coordinate plane by subtracting. Lesson 5 Effects of Changing Dimensions Proportionally Learning Target (LT-5) Describe how transformations change perimeter and area. Examples: Effects of changing ONE dimension. 1a. The height of a triangle is multiplied by 6. 1b. The diagonal SU of the kite is multiplied by ⅓.

7 Examples: Effects of changing dimensions proportionally 2a. The base and height of a rectangle with base 4ft and height 5ft are both doubled. 2b. The radius of J is multiplied by ⅕. 3. The base and height of the triangle with vertices P(2, 5), Q(2, 1), and R(7, 1) are tripled. Describe the effect on its area and perimeter. Effect of changing AREA. 4a. A circle has circumference of 32 π in. If the area is multiplied by 4, what happens to the radius? 4b. An equilateral triangle has perimeter of 21m. If the area is multiplied by ½, what happens to the side length? 5. Explain why the graph is misleading.

8 Effects of Changing Dimensions Proportionally Change in Dimensions Perimeter or Circumference Area All dimensions are multiplied by a P or C is multiplied by a Area is multiplied by a 2 One dimension is multiplied by a P is multiplied by a Area is multiplied by a Lesson 6 Geometric Probability Learning Target (LT-6) Calculate geometric probabilities. In geometric probability, the probability of an event is based on a ratio of geometric measures such as length or area. The outcomes of an experiment may be points on a segment or in a plane figure.

9 Examples: 1. A point is chosen randomly on PS. Find the probability of each event. a. The point is on RS. b. The point is not on QR. c. The point is on PQ or QR. 2. A pedestrian signal at a crosswalk has the following cycle: WALK for 45 seconds and DONT WALK for 70 seconds. a. What is the probability the signal will show WALK when you arrive? b. If you arrive at the signal 40 times, predict about how many times you will have to stop and wait more than 40 seconds. 3. Use the spinner to find the probability of each event. a. The pointer landing on yellow. b. The pointer landing on blue or red. c. The pointer not landing on green. 4. Find the probability that a point chosen randomly inside the rectangle is in each shape. Round to the hundredth. a. the circle b. the trapezoid c. one of the two squares

10 Chapter 9 Perimeter, Circumference, and Area Homework Assignments Lesson Problems 9.1 p. 594 #11-25, 28, 49, 52, 53, p. 603 #10-23, 26, 28-30, 40, 43, 44, 52, p. 609 #9-21, 31-33, 39, p. 620 #10, 13, 14, 16, 19, 24, p. 625 #8-17, 20, 24-27, p. 634 #16-30, 32, 34-37, 38*

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