UNIT 11. Angle Relationships, Area, and Perimeter/Circumference. CCM6 Name: Math Teacher: Projected Test Date:

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1 Page 1 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference UNIT 11 Angle Relationships, Area, and Perimeter/Circumference CCM6 Name: Math Teacher: Projected Test Date: MAIN IDEAS PAGE(s) Unit 11 Vocabulary 2 Perimeter of regular/ irregular figures (including missing dimensions) 3-6 Area of squares, rectangles, parallelograms, triangles and trapezoids (including missing dimensions) 7-15 Composite and Inscribed figures Area and Perimeter on the Coordinate Plane STUDY GUIDE

2 Unit 11 Vocabulary Page 2 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference perimeter area polygon regular polygon rectangle triangle hypotenuse parallelogram the measure around an object the amount of space inside a figure a closed plane figure formed by 3 or more line segments that intersect only at their endpoints a figure that has all equivalent sides and angles a parallelogram with four right angles a 3-sided polygon the longest side of a right triangle a four sided figure with opposite sides that are equal and parallel 2

3 Perimeter and Area Page 3 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference WARMUP: Answer the two questions and fill in the chart below. Complete this page and the next two. Mr. Bill s backyard is in the shape of a rectangle. It took him 600 feet of fence to enclose his back yard. If the length of the yard is twice as long as the width, what are the dimensions of Mr. Bill s yard? The Brown family has a square back yard with an area of 25 meters squared. They need to put a fence around it for their dog. How long will the fence be? Now, complete all you can on the next page. 3

4 Page 4 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference 4

5 Page 5 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference PERIMETER REVIEW What is it? How do I calculate it? PERIMETER AREA Find the Perimeter of each shape below. Find the length of the missing side if given the Perimeter of the whole shape. If the perimeter of a regular hexagon is 30cm, what is the length of one side? 5

6 Page 6 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference 6

7 Page 7 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference Perimeter Review, Area of Polygons The Relationship between Rectangles and Triangles 7

8 Page 8 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference Calculating Area of Squares/Rectangles/Parallelograms A parallelogram is just a in disguise! SHOW IT! Area formulas you need to KNOW: Shape Formula Example Solved Together Your Turn Square AREA= AREA= Rectangle AREA= AREA= Parallelogram AREA= AREA= 8

9 Page 9 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference WHAT BIG IDEA DO YOU NOTICE WITH TRIANGLES? 9

10 Page 10 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference On your calculator, type APPS Choose AreaForm Press any key twice Choose #1 Choose 3: Parallelogram After it defines the parallelogram, click the WINDOW key to see the area formula. When it finishes telling the formula, click the GRAPH key to see Why? Click GRAPH again. Do it again with #4: Triangle and check out #5 Trapezoid. **You don t have to know trapezoids. Here are two right triangles: Here are two non-right triangles: What shape do these create together? What shape do these create together? EVERY TRIANGLE DOUBLED MAKES EITHER A or a. Since a is really a tilted (same area), the area of a triangle is always of the area of a or a. FORMULA FOR THE AREA OF A TRIANGLE: A = ( ) Find the Area of each shape: 10

11 Page 11 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference REVIEW of AREA of TRIANGLES and PARALLELOGRAMS How do I find the area of a parallelogram? Area = base x height Since a parallelogram is similar to a rectangle, the base and height are relative to the length and width. * Be careful to measure the height and NOT the length of the slanted side. Parallelogram and its relation to a rectangle: (teachers: Demonstrate this using a piece of paper) Notice that when the outside piece is cut off and pasted to the other side of the parallelogram the polygon that is formed is a rectangle. Practice: H= 1.25 ft Area = bh Area = 2.5 x 1.25 Area = square ft B = 2.5 ft * remember to label with square units, because this is a two dimensional figure. Practice: 4.5 ft 4ft 12 ft Area = bh Area = 12 x 4 Area = 48 square feet. 11

12 Page 12 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference Practice: A parallelogram has these measures: Base = 4.1 inches Height = 2.2 inches Answer: 9.02 square inches Practice: A parallelogram has these measures: Base = 4 yd Height = 9 yd Answer: 36 How do I find the area of a triangle? Look at this rectangle When I split the rectangle in half what shapes are formed? Two triangles are formed when a rectangle is split in half. So, half of a rectangle is a triangle. So, half of the area of a rectangle is a triangle. Therefore, Area of a triangle = 1 bh 2 NOTE: Multiplying by 2 1 is the same as dividing by 2. You bh may see or use the formula like this: 2 Example: Area = ½ bh H = 10.5 m Area = 0.5 x 16.8 x 10.5 = B= 16.8 m Area = 88.2 sq. m or 88.2 m 2 *Remember this is still a two dimensional figure therefore your answer should be labeled in square units. 12

13 Page 13 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference Practice: Area = ½ bh H= 11 cm B = 6 cm Practice: The base of a triangle is 3 m and the height is 8 sq. m. What is the area? Start by writing the formula, then substituting for what you know. A = Practice: The base of a triangle is 8 cm and the area is 32 cm. What is the height of the triangle? (You will have to rearrange the formula) Start by writing the formula, then substituting for what you know. A = 13

14 HOMEWORK Day 2 Page 14 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference 14

15 Page 15 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference Area of Trapezoids On your TI-73, use the AREAFORM application and watch the area formula for trapezoids. Write what you discovered in the space below. 15

16 Page 16 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference Area of Composite Shapes WARMUP: What do we do if the shapes are MIXED? Mixed shapes are called COMPOSITE shapes. To find the area you have to. Total Area: square units (Hint: Get a ruler!) Find the area of the irregular polygon below. Measurements have been provided for you this time. 5 cm 4 cm 8 cm 2 cm 8 cm 4 cm 2 cm 10 cm 5 cm 16

17 Practice DRAW IT! Page 17 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference 1. Find the area of a right triangle with a base length of three units, a height of four units, and a hypotenuse of 5. HINT: the hypotenuse is always the biggest side and isn t part of the right angle. 2. Find the area of the trapezoid shown below using the formulas for rectangles and triangles A rectangle measures 3 inches by 4 inches. If the lengths of each side double, what is the effect on the area? 17

18 Page 18 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference 4. The lengths of the sides of a bulletin board are 4 feet by 3 feet. How many index cards measuring 4 inches by 6 inches would be needed to cover the board? 5. The sixth grade class at Hernandez School is building a giant wooden H for their school. The H will be 10 feet tall and 10 feet wide and the thickness of the block letter will be 2.5 feet. 1. How large will the H be if measured in square feet? 2. The truck that will be used to bring the wood from the lumberyard to the school can only hold a piece of wood that is 60 inches by 60 inches. What pieces of wood (how many and which dimensions) will need to be bought to complete the project? 6. A border that is 2 ft wide surrounds a rectangular flowerbed 3 ft by 4 ft. What is the area of the border? 18

19 Page 19 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference Area of Composite Shapes HOMEWORK 19

20 (Still Homework Day 3) Page 20 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference 20

21 Page 21 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference Area Formulas and Parts of Equations/Expressions Warm-up 21

22 Page 22 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference Shape within a Shape Game Cards 9) Calculate the area of the shaded section in the picture below: 15 cm 10) Mary s father put a garden in their backyard that had an area of 5 ft. by 9 ft. He put a sidewalk around the garden that had an area of 7 ft. by 12 ft. What is the area of the sidewalk around the garden? 9cm 4 cm 9 cm 11) Calculate the area of the shaded section in the picture below: 12 yd 18 yd. The dimensions of the inner polygon are 3 yd. by 9 yd. 12) The area of a local school is 3,844 sq. meters. When they built the school they put a sidewalk around the school. The dimensions of the rectangle formed by the outer edge of the sidewalk are 72 meters by 70 meters. What is the area of the space between the school and sidewalk? 22

23 Page 23 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference 13) Calculate the area of the shaded section in the picture below: The dimensions of the inner polygon are 8cm 12 cm by 5 cm 14) Bob built his very own lemonade stand in front of his house. His lemonade stand was 8 feet by 12 feet. He decided that he needed to make it look nicer by planting flowers all the way around the stand. The area of the rectangle formed around the planted flowers was 130 sq. feet. How much space was there between his lemonade stand and 11 cm the flowers? 15) Calculate the area of the shaded section in the picture below: 15 ft. 16) Regulation NCAA basketball courts have dimensions of 50 feet by 94 feet. There are chairs around the entire court that make up an area of cm The dimensions of the inner polygon are 3ft by 6 ft feet by 100 feet. How much space is there just for the chairs? 23

24 Page 24 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference ANSWERS for SHAPE WITHIN A SHAPE: 900 sq ft 34 sq ft 92 sq cm 189 sq yd 39 sq ft 162 sq. ft 1196 sq. m 5.495sq. ft sq ft sq in sq. ft sq. in sq. cm sq. ft 16.5 sq. cm 99 sq cm **Some answers above will not be used. 24

25 Page 25 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference 25

26 Page 26 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference 26

27 Page 27 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference Graph figure PQRS: P(-4, 3), Q(10, 3), R(10, -3), S(-4, -3). Determine the area and perimeter of the figure. Give the coordinates of a figure that has a perimeter half that of figure PQRS. Give the coordinates of a triangle that has an area half that of figure PQRS. Graph rectangle MNOP : M ( 4, 3), N(10, 3), O(4, 7), P(10, 7). Determine the perimeter and area of the figure. Give the coordinates for rectangle QRST that has the same area, but a different perimeter ABC ). Graph triangle : A ( 4,9), B(1,3), C(8,3 Determine the area of the triangle. Give the coordinates for a triangle DEF that has an area twice that of triangle ABC

28 Page 28 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference 28

29 Page 29 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference 29

30 Page 30 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference CCM6+ UNIT 8 STUDY GUIDE PERIMETER AND AREA Tell how to calculate the following. Write the formula if there is a formula! 1. Perimeter 2. Area of a square 3. Area of a rectangle 4. Area of a parallelogram 5. Area of a triangle What is different about the triangle formula? How will you remember this? 6. Area of mixed shapes what do you do? What is tricky? 30

31 WORD PROBLEMS Page 31 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference 13) The perimeter of a rectangle is 12. Determine a possible length and width, then calculate a possible area for that rectangle. 14) A rectangular photo is 5 inches long and 2 inches wide. Jimmy wants to enlarge the photo by doubling its length and width. How many inches of wood will he need to make a frame for the enlarged photo? 15) A figure is formed by a square and a triangle. Its total area is 32.5 m 2. The area of the triangle is 7.5 m 2. What is the length of each side of the square? a) 5 meters b) 25 meters c) 15 meters d) meters 16) A rectangle is formed by two congruent right triangles. The area of each triangle is 6 in 2. If each side of the rectangle is a whole number of inches, which of these could NOT be its perimeter? a) 26 inches b) 24 inches c) 16 inches d) 14 inches 17) The volume of a cube is found with the formula V=s 3 where the side length is represented by s. If the side length is 1 1 inches, what is the volume of the cube? 2 18) The perimeter of a rectangle is 20 ft 2. If the length is 5 ft, what is the AREA of the rectangle? 31

32 Page 32 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference For each problem: Plot the ordered pairs in the coordinate plane given Find the perimeter of the figure Find the area of the figure Find the distance between each point by using the absolute value method. 19. G (-4, 5) H (5, 5) I (-4, -5) J (5, -5) Perimeter of GHIJ: Area of GHIJ: 32

33 Page 33 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference 20. This figure is a four sided polygon. Before finding the area and perimeter find the missing point. R (-2, 2) S (4, 2) T (, ) U ( -2, -3) Perimeter of RSTU: Area of RSTU: What was the fourth vertex? How did you find the length for each side of the figure? Find the area of the shaded region for each figure below Find the Area and Perimeter. 33