GEOMETRY CHAPTER 10 STUDY GUIDE Areas of Rectangles, Parallelograms, and Triangles

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1 GEOMETRY CHAPTER 10 STUDY GUIDE Areas of Rectangles, Parallelograms, and Triangles Name Rectangle Draw & show how the polygon can be partitioned or transformed into a rectangle. Formula for Area Parallelogram Triangle 1. Find the area of each parallelogram. 15 cm 12 cm 8 cm 12 cm 20 cm 2. Find the value of h for the given parallelogram. 10 cm h in. 13 in. 12 in. 9 in 3. Find the area of each triangle. c) Equilateral triangle with side length 10 cm. 5 m 4 m 5 ft 8 m 2 ft 9 ft Geometry Chapter 10 Study Guide page 1 of 9

2 Areas of Trapezoids, Rhombuses/Rhombi, and Kites Name Trapezoid Draw & show how the polygon can be partitioned or transformed into a rectangle or a parallelogram. Formula for Area Rhombus Kite If the base and corresponding height are known, then A = If the diagonals are known, A = 1. Find the area of each trapezoid. 3 m 5 m 4 m 10 m 5 ft 3 2 ft Find the area of each rhombus. 3 in 2 in 4 ft 3. Find the area of each kite. 9 ft 2 cm 5 cm 3 cm 3 cm 2 cm 5 cm Geometry Chapter 10 Study Guide page 2 of 9

3 Areas of Regular Polygons 1. Define and draw an apothem of the regular polygon shown. 2. Draw a radius and label a central angle. 3. Find the perimeter and area of a pentagon with apothem 2 in. 4) Find the perimeter and area of a square with apothem 3 ft. 5. Find the perimeter and area of a hexagon with side length 8 cm. Geometry Chapter 10 Study Guide page 3 of 9

4 Perimeters and Areas of Similar Figures Investigations: 1. Draw a 2x3 rectangle. Calculate the perimeter and area of the rectangle. Double each side of the rectangle. Calculate the perimeter and area of the new rectangle. Compare the results with part a. What is the ratio of the perimeters of the new rectangle to the original rectangle? Ratio of areas? c) Triple each side of the rectangle in part a. Calculate the perimeter and area of the new rectangle. Compare the results with part a. What is the ratio of the perimeters of the new rectangle to the original rectangle? Ratio of areas? d) Halve each side of the rectangle in part a. Calculate the perimeter and area of the new rectangle. Compare the results with part a. What is the ratio of the perimeters of the new rectangle to the original rectangle? Ratio of areas? Geometry Chapter 10 Study Guide page 4 of 9

5 e) Record the result of parts b-d in the table shown below for the first three rows. Examine the patterns and fill in the remaining rows. If each side is multiplied by Similarity ratio (scale factor) of new to original rectangle Ratio of Perimeters (New to Original) Ratio of Areas (New to Original) k a b Theorem 10-7: If two polygons are similar with the lengths of corresponding sides in the ratio of a:b, then (1) the ratio of their perimeters is, and (2) the ratio of their areas is. 1. Find the ratio of the perimeters and the ratio of the areas of the squares. 2 cm 5 cm 2. The similarity ratio of two similar polygons is 3:4. If the perimeter of the smaller polygon is 12 cm, what is the perimeter of the larger? If the area of the smaller polygon is 36 cm 2, what is the area of the larger? 3. If it costs $200 to fence a 10 ft by 15 ft rectangular garden, how much does it cost to fence a 30 ft by 45 ft garden? If it costs $40 to fertilize a 10 ft by 15 ft rectangular garden, how much does it cost to fertilize a 30 ft by 45 ft garden? Geometry Chapter 10 Study Guide page 5 of 9

6 1. Vocabulary Central angle (pg 566) Circles and Arcs Minor arc Measure of a minor arc Major arc Measure of a major arc Semicircle Concentric Circles (pg 568) Arc length (pg 569) 2. Formulas: Circumference of a circle: Arc Length: 1. Find the indicated measures: Find mbc, mbdc, mbde, and length of BC. Circumference =? C E D A 70 3 A 45 3 C B B Geometry Chapter 10 Study Guide page 6 of 9

7 2. Use the data in the table and a protractor to construct a circle graph. Activity Number of hours per day School 7 Eat 2 Recreation 3 Sleep 8 Others 4 3. A running track consists of a rectangle and two congruent semicircles as shown. What is the total distance (in yards) around the track? Round your answer to the nearest tenth. 110 yd 50 yd 110 yd 4. A wheel has diameter 2 feet. How many revolutions does it make if it travels 100 feet? Geometry Chapter 10 Study Guide page 7 of 9

8 Areas of Circles and Sectors Formulas: Area of circle: Area of sector: 1) Find the area of the shaded sector. 2) Find the area of the shaded region. A C B 5 cm 2) Find the area of the region between the square and the circle. 3) A cow is tethered at a corner of a square grass field of length 100 feet. How long must the rope be so that the cow would have access to exactly half of the field? 4 3) Find the area of the region between the regular hexagon and the circle. The circle has radius 6 ft. Geometry Chapter 10 Study Guide page 8 of 9

9 Geometric Probability Probability of an event (pg 582): Geometric Probability: 1. Probability and Length: Let AB be a segment that contains the segment CD. If a point K on AB is chosen at random, then the probability that it is on CD is as follows: P(point K is on CD) = 2. Probability and Area: Let J be a region that contains region M. If a point K in J is chosen at random, then the probability that it is in region M is as follows: P(point K is in region M) = 1) Suppose that your school day begins at 7:30 a.m. and ends at 2:15 p.m. You eat lunch at 11:30 a.m. If there is a fire drill at a random time during the day, what is the probability that it begins after lunch? 2) A bus runs every 25 minutes. If a passenger arrives at the bus stop at a random time, what is the probability that he/she will have to wait at least 15 minutes for the bus? 3) Find the probability that a chosen point in the figure lies in the circle At a carnival game, to win a prize, you must toss a coin so that it lands entirely within the circle shown below. If the coin has radius ½ inch, find the probability of winning on one toss. Assume that the center of the tossed coin is equally likely to land at any one point within the rectangle. In order to win a prize, about how many tosses would you expect to make? 5 in 20 in 40 in Geometry Chapter 10 Study Guide page 9 of 9

Postulate 17 The area of a square is the square of the length of a. Postulate 18 If two figures are congruent, then they have the same.

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