CN#5 Objectives 5/11/ I will be able to describe the effect on perimeter and area when one or more dimensions of a figure are changed.

Transcription

1 CN#5 Objectives I will be able to describe the effect on perimeter and area when one or more dimensions of a figure are changed. When the dimensions of a figure are changed proportionally, the figure will be similar to the original figure. I will be able to apply the relationship between perimeter and area in problem solving. Example 1: One Dimension Describe the effect of each change on the area of the given figure. The height of the triangle is multiplied by 6. original dimensions: multiply the height by 6: Helpful Hint If the radius of a circle or the side length of a square is changed, the size of the entire figure changes proportionally. = 30 in 2 = 180 in 2 Notice that 180 = 6(30). If the height is multiplied by 6, the area is also multiplied by 6. 1

2 Example 2A: Dimensions Proportionally Describe the effect of each change on the perimeter or circumference and the area of the given figures. The base and height of a rectangle with base 4 ft and height 5 ft are both doubled. original dimensions: P = 2(4) + 2(5) = 18 ft A = (4)(5) = 20 ft 2 dimensions doubled: Example 2A Continued P = 2b + 2h A = bh P = 2(8) + 2(10) = 36 ft 2(4) = 8; 2(5) = 10 A = (8)(10) = 80 ft 2 The perimeter is multiplied by 2. 2(18) = 38 The area is multiplied by 2 2, or 4. 4(20) = 80 Example 3A: Area A circle has a circumference of 32π in. If the area is multiplied by 4, what happens to the radius? The original radius is and the area is A = πr 2 = 256π in 2. If the area is multiplied by 4, the new area is 1024π in 2. πr 2 = 1024π Set the new area equal to πr 2. r 2 = 1024 r = 1024 = 32 Divide both sides by π. Take the square root of both sides and simplify. Notice that 32π = 2(16π). The radius is multiplied by 2. CN#6 Objectives I will be able to calculate geometric probabilities and use them to predict results in real-world situations. 2

3 Remember that in probability, the set of all possible outcomes of an experiment is called the sample space. Any set of outcomes is called an event. If every outcome in the sample space is equally likely, the theoretical probability of an event is Geometric probability is used when an experiment has an infinite number of outcomes. 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. Remember! If an event has a probability p of occurring, the probability of the event not occurring is 1 p. 3

4 Example 1A: Using Length to Find Geometric Example 1B: Using Length to Find Geometric A point is chosen randomly on PS. Find the probability of each event. The point is not on QR. The point is on RS. Subtract from 1 to find the probability that the point is not on QR. Example 1C: Using Length to Find Geometric Example 4: Using Area to find Geometric Find the probability that a point chosen randomly inside the rectangle is in each shape. Round to the nearest hundredth. The point is on PQ or QR. P(PQ or QR) = P(PQ) + P(QR) 4

5 Example 4A: Using Area to find Geometric Example 4B: Using Area to find Geometric the circle The area of the circle is A = πr 2 The probability is P = = π(9) 2 = 81π ft 2. the trapezoid The area of the trapezoid is The probability is Example 4C: Using Area to find Geometric one of the two squares The area of the two squares is A = 2s 2 = 2(10) 2 = 200 ft 2. The probability is 5