Chapter 2: Sec. 2.2.1: How can | measure an object?\f261. Length often provides a direct way to answer the question= \"How big?\" In this activity= your teacher will give your team rulers with a unit of length to use to measure distances. For instance. if you have an object that has the same length as three of your units placed next to one another= then the objects length is "'3 units.\" a. Common units you may have used before are inches or meters. However= your unit does not match any of the familiar units. Give your unit of measure a unique name. Then continue marking and labeling units on your ruler as accurately as possible. b. The dimensions of a figure are its measurements of length. For example= the measurements in each figure below describe The relative size of each object. 8 cm 10 cm 2 cm I Dimensions can describe how long= Wide= or tall the object is by measuring OT: dimensions C311 be found by measuring a length that is not a side. the lengths ofthe edges. Find The dimensions of the shape on the Lesson 2.2.1A Resource Page using your unit of length. That is= how wide is the shape? How tall? Compare your results with Those of oTher Teams. What happened? c. The local baseball club is planning to make a mural that is the same general shape as the one you measured in part w (b) (but fortunately a much larger version!) The club plans to frame the mural with neon tubes. Approximately 'a t, how many units of neon tube will they need to do This? 1"\" g. '7'; .a {h 2-66. Examine the diagram at right. Then use the information provided in the diagram to find the measures of angles a, b, c, and d. For each angle, name the relationship from your Angle Relationships Toolkit that helped justify your conclusion. For example, did you use vertical angles? If not, what type of angle did you use? Homework Help \\ 2-67. Examine the triangle at right. Homework Help \\ D a. If m/D = 480 and m/F = 117, then what is mZE? E b. Solve for r if m/D = 4x + 20, m/F = 7x - 80, and mZE = 4x + 6. Then find m/D. F c. If m/D = mZF = mZE, what type of triangle is AFED?268. Plot AABC on graph paper if Am, 3], 3(2, 1}= and C(5, 7]. 268 Hl-T'eTooE (Desmos) Homework HelL'k a. AABC is rotated about the origin 180 to become AA'B'C". Name the coordinates of 44': B\2-70. STRATEGIES TO MEASURE AREA In Lesson 2.2.1 you used a grid to measure area. But what if a grid is not available? Or what if you want an exact measurement? Examine the variety of shapes below. Work with your team to find the area of each one. If a shape has shading, then find the area of the shaded region. Be sure to listen to your teammates carefully and look for different strategies. Be prepared to share your team's method with the class. a b 8' 3' 12 m 4 m 8 m 11 24 m C. d. 2x + 3 18 cm 27 cm e. f 5 yds 14 yds 10"2-72. How do you know which dimensions to use when finding the area of a triangle? a. Copy each triangle below onto your paper. Then find the area of each triangle. Draw any lines on the diagram that will help. Turning the triangles may help you discover a way to find their areas. (1) (2) (3) 5mm 43 mm 9 m 5.9" 5 m -14 mm 6.8" 7" 2 m 6 m b. Look back at your work from part (a). Which numbers from each triangle did you use to find the area? For instance, in the center triangle, you probably used only the 6.8 " and 5.9" . Write an explanation and/ or draw a diagram that would help another student understand how to choose which lengths to use when calculating the area. c. Mario, Raquel, and Jocelyn are arguing about where the height is for the triangle below. The three have written their names along the part they think should be the height. Determine which person is correct. Explain why the one you chose is correct and why the other two are incorrect. Raquel Jocelyn Mario2-74. Review how to multiply binomials by reading the Math Notes box for this lesson. Then rewrite each of the expressions below by multiplying binomials and simplifying the resulting expression. Homework Help a. (4x + 1) (2x - 7) b. (5x - 2) (2x + 7) c. (4x - 3) (x - 11) d. (-3x + 1) (2x - 5) 2-75. The shaded triangle at right is surrounded by a rectangle. Find the area of the triangle. Homework Help \\ 8' 434+ 2-76. For each diagram below, solve for r. Explain what relationship(s) from your Angle Relationships Toolkit you used for each problem. Homework Help a. b . 6x 5x + 130/3x + 70 4x + 10 C. d 3x + 50 2x + 180 2x+170 30