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 Targets LT9-1: Solve problems involving the perimeter and area of triangles and special quadrilaterals. Success Criteria Find measurements of parallelograms. Find measurements of triangles and trapezoids. Find measurements of rhombuses and kites. **Refer to the formula sheet for area formulas. Ex#1: Find measurements of parallelograms. A. Find the area of the parallelogram. B. Find the height of a rectangle in which b = 3 in and A = (6x x 6) in 2. C. Find the perimeter of the rectangle in which A = (79.8x 2 42) cm 2.
2 Ex#2: Find measurements of triangles and trapezoids. A. Find the area of a trapezoid in which b 1 = 8in, b 2 = 5in, and h = 6.2in. B. Find the base of the triangle in which A=(15x 2 )cm 2. C. Find b 2 of the trapezoid, in which A = 231mm 2. Ex#3: Find measurements of rhombuses and kites. A. Find d 2 of a kite in which d 1 = 14in and A = 238in 2. B. Find the area of the rhombus. C. Find the area of the kite.
3 Ex#4: Solve application problems involving the perimeter and area of triangles and special quadrilaterals. 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 Targets LT9-2: Apply the formula for the area and circumference of circles and the area and Success Criteria Find measurements of circles. Find the area of a regular polygon. Circle: Center of a Circle: π Center of a Regular Polygon Apothem: Central Angle of a Regular Polygon: Ex#1: Find measurements of circles. A. Find the area of K in terms of π.
4 B. Find the radius of J if the circumference is (65x + 14)π m. C. Find the circumference of M if the area is 25x 2 π ft 2. Ex#2: Find the area of a regular polygon. A. Find the area of a regular heptagon with side length 2 ft. Round to the nearest tenth. B. Find the area of a regular hexagon with apothem 6 cm. Round to the nearest tenth.
5 Lesson 3 Composite Figures Learning Targets LT9-3: Find the area of composite figues and estimate the areas of irregular shapes. Success Criteria Find the areas of composite figures by adding. Find the areas of composite figures by subtracting. Solve application problems involving composite figures. Estimate areas of irregular shapes. Composite Figures: Ex#1: Find the areas of composite figures by adding. Round to the tenths. A. B. Ex#2: Find the area of composite figures by subtracting. Round to the tenths. A. B.
6 Ex#3: Solve application problems involving composite figures. 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? Ex#4: Estimate the areas of irregular shapes. Use a composite figure to estimate the shaded area. The grid has squares with a side length of 1ft. Lesson 4 Perimeter and Area in the Coordinate Plane Learning Targets LT9-4: Find the area and perimeter of figures in the coordinate plane. Success Criteria Estimate areas of irregular shapes in the coordinate plane. Find perimeter and area in the coordinate plane. Find areas in the coordinate plane by subtracting. 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.
7 Ex#1: Estimate areas of irregular shapes in the coordinate plane. A. Estimate the area of the irregular shape. B. Estimate the area of the irregular shape. Ex#2: Find perimeter and area in the coordinate plane. A. Classify the polygon below. Find the perimeter and area of the polygon. B. Classify the polygon below. Find the perimeter and area of the polygon.
8 Ex#3: Find areas in the coordinate plane by subtracting. A. B. Lesson 5 Effects of Changing Dimensions Proportionally Learning Targets LT9-5: Describe how transformations change perimeter and area. Success Criteria Describe effects of changing one dimension. Describe effects of changing dimensions proportionally. Describe the effects of changing the area. Ex#1: Describe the effects on the area of a figure by changing ONE dimension. A. The height of a triangle is multiplied by 6. B. The diagonal SU of the kite is multiplied by ⅓.
9 Ex#2: Describe the effects on the perimeter and area of a figure by changing dimensions PROPORTIONALLY. A. The base and height of a rectangle with base B. The radius of J is multiplied by ⅕. 4ft and height 5ft are both doubled. C. 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.
10 Ex#3: Describe the effects of changing the area. A. A circle has circumference of 32 π in. If the area is multiplied by 4, what happens to the radius? B. An equilateral triangle has perimeter of 21m. If the area is multiplied by ½, what happens to the side length? Effects of Changing Dimensions Change in Dimensions Perimeter or Circumference Area One dimension is multiplied by a Area is multiplied by a All dimensions are multiplied by a P or C is multiplied by a Area is multiplied by a 2 Lesson 6 Geometric Probability Learning Targets Success Criteria LT9-6: Calculate geometric probabilities. Use length to find geometric probability. Apply geometric probability to real situations. Use angle measure to find geometric probability. Use area to find geometric probability. 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.
11 Ex#1: Use length to find geometric probability. 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. Ex#2: Apply geometric probability to real situations. 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.
12 Ex#3: Use angle measure to find geometric probability. 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. Ex#4: Use area to find geometric probability. 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 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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