MATH Integrated Math I  - Unit 22: Perimeter, Circumference, and Area
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Perimeter

1) What is the perimeter of the parallelogram? (Recall:  The opposite sides of a parallelogram are congruent.)

2) Which formula could be used to find the perimeter of the square?

For the next two problems, find the perimeter. Be sure to label the answers correctly.

3) What is the perimeter of the triangle?

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4) What is the perimeter of the rectangle?

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5) For each figure below, the lengths of two or three sides are given.  Segments that appear to be perpendicular are perpendicular. Which figure could have a perimeter of 28? State the letter of the correct answer.

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6) Jackie cannot keep her dogs from wandering over to the neighbor’s house.  Being a polite neighbor, Jackie decides to build a fence so that her pets will stay on their own property.  Jackie’s property is laid out in the shape of a parallelogram, as shown in the illustration below.  She plans to build the fence around the property, EXCLUDING the woods.  The dimensions of Jackie’s property are given in the illustration shown below.  How much fencing will Jackie need to buy? 

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Circumference

 Investigation: In your home or school, find three circular objects or objects that have a circular base, such as a can of soda, a roll of paper towels, etc. Pen/pencil, paper, and a ruler are also needed.  Complete the following steps for all three objects. Record the measurements in an organized chart such as the one given, and then answer the next two questions.

7) True or False.  In the given statement, if it is true, state True. If the statement is false, state False and give a number that will make the statement true.

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8) The ratio of C / d is given the special name “Pi”.  The value of Pi is generally given as 3.14 even though this is a rounded number. “Pi” is equal to the ratio of any circle’s circumference to its diameter.  Research the Internet and find the first 50 digits of “pi”.  Copy and paste them in the text box below.

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9) In the steps provided below, “C” represents circumference, “d” represents diameter, and  “r” represents radius.  Explain why both “C = pi times d” and “C = 2 times pi times r” are both formulas that can be used to find the circumference of a circle.

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For the next four questions related to circumference, label the answers correctly and round the answers to the nearest tenth, when necessary. Use 3.14 for “pi”.

10) What is the circumference of a circle with a diameter of 12.6 inches?

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11) What is the circumference of a circle with a radius of 15.8 centimeters?

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12) What is the radius of a circle if its circumference is 41.8 feet? Express the answer rounded to the nearest tenth of a foot.

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13) One lap around the outside of a circular track is 421 yards. If Ben jogs from one side of the track to the other, through the center, about how far would he travel?

Area

The formulas for finding the area of several two-dimensional shapes are given below.  Use them as needed to solve the following problems about area.

14) Study the diagram below, and then answer the following question: The area of a triangle is what fractional part of the area of a rectangle that has the same base and height?

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15) Explain how the formula for the area of a square can be derived from the formula for the area of a rectangle?

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For the next four questions, find the area of the given figure. Be sure to label the units correctly. For example: 68 square centimeters may be abbreviated as 68 sq cm.

16) What is the area of the triangle?

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17) What is the area of the parallelogram?

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18) What is the area of the trapezoid?

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19) What is the area of the square?

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20) The base and height of a triangle is doubled. How is the area affected? 

21) Which figure does NOT have an area of 114 square feet? State the letter of the correct answer.

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22) Graph the ordered pairs: A(–1, –1), B(4, –1), C(1, 3), D(–1, 3). Then join the points in the following order: A, B, C, D, A. (a) What is the name of the figure? (b) What is the figure’s area?

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23) In the steps shown below, the formula to find the area of a triangle has been transformed into a formula to find the height (h) of a triangle when given the area (A) and the base (b). Answer the following questions: (a) What is missing in the reason for step #2? (b) What is missing in the reason for step #4?

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24) What is the height of a triangle with a base of 7.2 meters and an area of 32.4 meters?

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25) A trapezoid has an area of 120 square feet. If the bases are 14 feet and 16 feet, what is the height? The solution to this problem is started below; but, it is not finished.  Finish the problem. 

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26) What is the cost of carpeting a hallway that measures 15 feet by 4 feet at $21 per SQUARE YARD?  (Hint:  Find the area in square feet, then convert to square yards before calculating the cost.)

For the remaining problems that are related to the area of circles and circle sectors, use 3.14 for “pi”.  Label all answers correctly and round the answers to the nearest hundredth, if necessary.

27) What is the area of the circle?

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28) What is the area of the circle? (Note:  A diameter is given in the figure, so adjust this value to a radius for use in the formula for area of a circle.)

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29) A pizzeria has three specials: Special 1: One large pizza for $12.50, Special 2: Two medium pizzas for $12.50, and Special 3: Three small pizzas for $12.50. Use the figure shown below to determine which offer is the best buy. State the answer and explain how you derived your answer.

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Area of a Circle Sector

30) What is the area of three of the eight sectors in the circle shown below?

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31) A circle has a radius of 8 inches and its area is divided into five equal sectors. What is the area of four of the sectors?

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Area of a Composite Shape

For the last two questions, find the area of the shaded region. Round the answers to the nearest tenth. (Hint: Find the area of the outer shape and subtract away the area of the inner shape.)

32) What is the area of the shaded region (teal-colored area)? (Hint:  The shaded region is the is the area of the larger circle with the area of the smaller circle cut out.)

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33) What is the area of the shaded region (burgundy-colored area) inside the circle and outside of the square?

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