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Guided Notes – Perimeter and Area Date_________ Perimeter – ________________________________________________________ Area – the number of __________________________________ a figure encloses If the problem asks about: A fence A pool cover Painting a wall Traveling around Rectangles: 1) What is the perimeter and area of this rectangle? 2) What is the perimeter & area of this rectangle? P = _______ P = ___________ A = _______ A = __________ 3) The area is 45 square feet. What is the width? 4) The perimeter is 60 feet. What is the length? Equation ______________ Answer__________ Equation ______________ Answer__________ Squares: 1) Parallelograms: 1) A parallelogram has a 9 cm base and a height of 10 cm. Draw the parallelogram and find its area. 2) 2) The parallelogram below has an area of 40 square units. Find the perimeter of the parallelogram. 2) The area of a triangle is 24 inches. If the triangle has a height of 6 inches, find the base. Then find the perimeter. Triangles: 1) Formula ___________ Area ________ Perimeter ________ Formula __________________ Base __________ Perimeter ___________ Trapezoids: 1) 2) Formula _____________________ Formula _____________________ Answer ____________________ Answer ____________________ 4) 3) Formula _____________________ Formula _____________________ Area ____________________ Area ____________________ Perimeter _________________ Perimeter _____________________ Guided Notes – Perimeter and Area Date_________ Perimeter – ________________________________________________________ Area – the number of __________________________________ a figure encloses If the problem asks about: A fence A pool cover Painting a wall Traveling around Rectangles: 1) What is the perimeter and area of this rectangle? 2) What is the perimeter & area of this rectangle? P = _______ P = ___________ A = _______ A = __________ Using Equations with Perimeter and Area 1) The area is 45 square feet. What is the width? 2) The perimeter is 60 feet. What is the length? Equation ______________ Equation ______________ Answer__________ 3) Answer__________ x + 12 The area of the rectangle is 58 square units. Solve for x. Equation ______________________________ Simplified _______________________________ 4 Answer ____________ Find the perimeter ______________________________ 3x + 12 4) The area of the rectangle is 233.1 square units. Solve for x. Equation ______________________________ Simplified _____________________________ Answer ____________ Find the perimeter _______________________ 10.5 Squares: 1) The square shown below has a perimeter of 84 cm. Find a. Then find the length of each side. 2) The square shown below has a perimeter of 44 cm. Find a. Then find the length of each side. a+3 2a + 9 Equation ______________ Equation ______________ Simplified_______________ Simplified_______________ Answer__________ Answer__________ Length __________ Length __________ 3) Joanna is tiling a floor. The floor measures 9 feet by 4 feet. Joanna is using square tiles with sides that measure 6 inches. How many tiles will it take to cover the entire floor? 4) Triangles: 1) Formula _______________ 2) Formula _____________ Area ___________ Area ___________ Perimeter ___________ Perimeter ___________ 3) The area of a triangle is 24 square inches. If the triangle has a height of 6 inches, find the base. 4) The area of a triangle is 16 square inches. If the triangle has a height of 8 inches, find the base. Formula __________________ Formula __________________ Base __________ Base __________ 5) The area of the triangle is 114 square units. Solve for x. Then find the perimeter. Equation ______________________________ Simplified _____________________________ Answer ____________ Perimeter _______________ Guided Notes – Area of Composite Shapes Date_________ Composite Shapes: Two or more shapes put together 1) 2) To find the area: 1. ___________________ 2. Find the area of each part 3. ____________________ 3) 4) 5) To find the area of the “shaded region” 1. Find the area of _________________________ 2. Find the area of __________________________ 3. ____________________ 1) Group 1 Group 2 1. Find the area and perimeter 1. Find the area and the perimeter A ______ P ______ A ______ P ______ 2. Find the area and perimeter A ______ P ______ 2. Write an expression for the area and perimeter A __________ 3. Find the area and perimeter P __________ A ______ P ______ 4. Find the area 5. Find the area of the shaded region. 4. 3. Find the area of the shaded region. Guided Notes – Area and Circumference of Circles Date_________ Circles: Terms to Know – Radius ________________________ 1) The radius of a circular table is 13 inches. What is the diameter of the table? Diameter ______________________ 2) The diameter of a circle is 25. What is the radius? Area ____________________________________ Formula _______________ Circumference ____________________________ Formula ______________ 1) A = __________ 2) A = __________ C = __________ C = __________ 3) A = __________ C = __________ 4) A = __________ C = __________ Word Problems: 1) 2) Astronauts train for space flight in a centrifuge, which consists of a rotating arm with a cab at the outer end of the arm. The arm, which has a length of 58 feet, is revolved about the center of the centrifuge. An astronaut sits in the cab, which is then rotated 50 times per minute. To the nearest hundred feet, how far does the astronaut travel in one minute? 3) 14 in 18 in 10 in Which pizza is the better buy per square inch? *Hint: Find the area of each, then find price per square inch. Large: A = _________ Medium: A = __________ Small: A = __________ $/in² = ________ $/in² = ________ $/in² = ________ 4) d = 8 in d = 10 in $10.00 $14.25 At the village, Ava is deciding whether to buy a full 10 inch (diameter) apple pie for $14.25 or a half a pumpkin pie for $10.00. Which one is the better buy per square inch? Apple: A = _________ 5) $/in² = ________ Pumpkin: A = __________ $/in² = ________ Guided Notes – Area and Circumference of Circles Date_________ Circles: Terms to Know – Radius ________________________ 1) The radius of a circular table is 13 inches. What is the diameter of the table? Diameter ______________________ 2) The diameter of a circle is 25. What is the radius? Area ____________________________________ Formula _______________ Circumference ____________________________ Formula ______________ 1) A = __________ 2) A = __________ C = __________ C = __________ 4) 3) A = __________ A = __________ C = __________ C = __________ Semicircles: Find the area or circumference and ________________________________________ 5) 6) A = __________ C = __________ A = __________ C = __________ Word Problems: 1) 14 in 18 in 10 in Which pizza is the better buy per square inch? *Hint: Find the area of each, then find price per square inch. Large: A = _________ $/in² = ________ Medium: A = __________ Small: A = __________ $/in² = ________ $/in² = ________ 2) d = 8 in d = 10 in $10.00 $14.25 At the village, Ava is deciding whether to buy a full 10 inch (diameter) apple pie for $14.25 or a half a pumpkin pie for $10.00. Which one is the better buy per square inch? Apple: A = _________ $/in² = ________ Pumpkin: A = __________ $/in² = ________ Guided Notes - Composite Shapes with Circles or Semicircles 1) 2) Top Piece ______ Date_________ Top Piece ______ Middle Piece _______ Bottom Piece _______ Bottom Piece _______ Total Area _______ Total Area _______ 4) 3) Top Piece ______ Top Piece ______ Bottom Piece _______ Bottom Piece _______ Total Area _______ Total Area _______ 5) 6) Left Piece ______ Top Piece ______ Right Piece _______ Bottom Piece _______ Total Area _______ Total Area _______ 7) 8) Find the area of the shaded region. Outer _________ Outer _________ Inner __________ Inner __________ Shaded Area _______ Shaded Area _______ Word Problems 1) 2) 3) Level 1 Find the perimeter and area of the shapes. 1. 2. 3. 3 a+4 Level 2 1. 2. Find the area of the composite shape below. Level 3 Find the approximate price per square inch to find the better deal Pizza Hut Donato’s d = 10 in, cost = $15 cost = $17 Jet’s d = 15 in, cost = $25 Level 4 Find the area of the shapes. 1. Level 5 2. 2. Find the area of the shape below 1. Level 6 1. Find the area of the shaded region if the diameter of the smaller circles is 2. 2. Find the area of the composite shape below. . Level 7 Find the area of the shapes 1. 2. Level 8 1) Area = __________ Level 9 1) She is going to use square tiles that are 6 inches on each side. How many tiles will she need? Stove 2 ft 4 ft 10 feet 2) Mrs. Graf wants to tile her kitchen seen at right. She will tile the entire floor except for where her sink, stove and island will be. What is the area of the floor she will have to tile? 2 ft 3.5 ft 4 ft Sink 5 ft Island 12 feet Level 10 Find the area of the shaded portion in the figures below. 1. 2. 8 cm 10 cm Level 11 Find the area of the shaded portion in the figures below. 1. 2. Level 12 Find the area of the shaded portion in the figures below. 1. 2. Level 13 1. Find the area of the shaded region. A = _______________ 2. Find the circumference of the circle. C = ________________ Level 14 1. Find the area of the shaded region. A = _______________ 2. Find the circumference of the circle C = ________________ Level 15 1. Find the area of the shaded region. A = _______________ 2. Find the circumference of the semi - circle. C = ________________ 1) 2) Level 17 Find the area and perimeter of the composite shapes below. 1) 2) Area = __________ Area = __________ Perimeter = _________ Perimeter = _________ Name____________________ Composite Shape Levels Level 1 1) Area = __________ Perimeter = _________ Level 7 2) Area = __________ 1) Area = __________ Perimeter = _________ Perimeter = _________ 3) Area = __________ 2) Area = __________ Perimeter = _________ Perimeter = _________ Level 2 1) __________ 2) _________ Level 8 1) __________ 2) __________ Level 3 Donato’s: $______/in² Level 9 Pizza Hut: $______/in² Jets: $______/in² 1) __________ Best Buy ______________ 2) __________ Level 10 1) __________ Level 4 1. __________ 2. __________ Level 5 2) __________ Level 11 1) __________ 2) __________ 1. Area = __________ 2. Area = _________ Level 12 1) __________ Level 6 1. Area = __________ 2. Area = _________ 2) __________ Guided Notes – Using Algebra to Find Missing Dimensions Together 1. A rectangle has an area of 120 square inches and a length of 12 inches. Calculate the width and perimeter. On Your Own 1. A rectangle has an area of 94.5 square inches and a length of 7 inches. Calculate the width and perimeter: Equation ______________________ Equation ______________________ Width ________________ Width ________________ Perimeter _______________ Perimeter _______________ 2. A rectangle has a perimeter of 72 inches and a length of 19 inches. Calculate the following: 2. A rectangle has a perimeter of 28 square and a length of 9 inches. Calculate the following: Equation ______________________ Equation ______________________ Width ________________ Width ________________ Area _______________ 3. A triangle has an area of 15.75 square inches and a base of 7 inches. Write an equation to solve for the height. Area _______________ 3. A triangle has an area of 40 square inches and a base of 10 inches. Write an equation to solve for the height. Equation ______________________ Equation ______________________ Height _______________ Height _______________ Use 3.14 as pi. 4. Find the radius and diameter of the circle if the circumference is 25.12 cm. 5. Date_________ What is the area of the circle if its circumference is 157 meters? 4. Find the radius and diameter of the circle if the circumference is 20.41 cm. 5. What is the area of the circle if its circumference is 62.8cm? Together DO NOT use 3.14 as pi. Give your answers in terms of pi. 6. Find the area of the circle if the circumference is 25𝜋. 7. The circumference of the semicircle is 37.68m. Find the area of the shaded region. Round to the nearest tenth. On Your Own DO NOT use 3.14 as pi. Give your answers in terms of pi. 6. Find the area of the circle if the circumference is 18𝜋. 7. Find the area of the shaded region if the circumference of the circle is 56.52 cm. Area, Perimeter and Circumference Quiz Review Name: _____________________ Level 1 Directions: Find the perimeter and area of the following shapes. (Try to do it without using your formulas!) 2. 1. P = __________ 3. P = __________ P = __________ A = __________ A = __________ A = __________ Level 2: Better Buy Find the approximate price per square inch to find the better deal Jet’s d = 15 in, cost = $25 Pizza Hut cost = $17 Donato’s d = 10 in, cost = $15 Level 3: 3. Find the area and circumference/perimeter of the circles and semicircles 1. C = __________ A = __________ 2. C = __________ A = __________ Level 4: Work backwards to solve the following problems: 1) A realtor advertises the office space in a building as 1,400 square feet. The office space is rectangularly shaped. What is the length of the side of the office space if the width is 35 feet? 2) A rectangle has an area of 92 square inches and a length of 11.5 inches. What is the width? 3) A rectangle has a perimeter of 54 square inches and a length of 13 inches. What is the width? Level 5: Find the area of the composite shapes 1. The object is symmetrical through Z. X = 13 in, Y = 18 in, Z = 17 in, H = 9 in 3. 2. A = __________ A = __________ A = __________ Level 6: Find the area and perimeter of the composite shapes 1. 3. 2. P = __________ P = __________ P = __________ A = __________ A = __________ A = __________ Level 7: Find the area of the shaded region in the figures below. 1. A = __________ 3. 2. A = __________ A = __________ Level 8: Work backwards to solve the following problems: 1) A sign is in the shape of a triangle. It has a base of 16 inches and an area of 96 square inches. What is the height of the sign? 2) The area of a circular clock is 200.96 square inches. Find the radius _________ Find the circumference _________ 3) The circumference of a circular pool is 43.96 feet. Find the radius _________ Find the area_________ Guided Notes – Cross Sections Date ___________ Cross Section: A plane that intersects or ___________________ a _____________,forming a two-dimensional figure Your Goal: Be able to identify or draw the _____________________ of the cross section. *You can slice many different ways: A) Vertically (__________) B) Horizontally (__________) Example 1: A square pyramid cut _______________ makes a cross section that is a ______________. C) Diagonally (__________) Example 2: A plane cuts the triangular pyramid ______________. What is the shape of the cross section? Example 3 : A plane cuts the cylinder vertically. What is the shape of the cross section? Example 4: A plane cuts a right rectangular prism (_______) diagonally. What is the shape of the cross section? *The vertical and horizontal slices can be made: D) Through the ______________ Example 1: A square pyramid cut vertically through the apex makes a cross section that is a _______________ AND E) Not through the _______________________ Example 2: A square pyramid cut vertically (but not through the apex) makes a cross section that is a _______________ Test Example *Hint: Could be made through the apex and NOT through the APEX: F) Cross sections can be parallel or _______________________ to the _____________ of the solid. PARALLEL _______________________________________________________ PERPENDICULAR _________________________________________________ 1) A triangular right prism is cut perpendicular to the base. What is the shape of the cross section? Parallel to the base? 2) What cross section is formed when a plane intersects a square pyramid so that it is perpendicular to the base? Parallel to base? G) Cross sections can be through certain ________________________________________. 1) What shape is made when the cross section below is cut through points ABCD? 2) What shape is made when the cross section below is cut through points EFG? Guided Notes – Surface Area and Volume Rectangular Prisms Date ____________ Surface Area: The area of each ____________________________ of a solid. Volume: The _____________________ units a solid takes up. Front _______ 1) Back________ 7 Side ________ Side ________ 4 20 Bottom_______ Volume ______ 2) Top ________ Surface Area = ________ Front _______ Back________ Side ________ Side ________ Top ________ Bottom_______ Surface Area = ________ 3) Volume ______ Front _______ Back________ Side ________ Side ________ Top ________ Bottom_______ Surface Area = ________ Volume ______ 4) Front _______ Back________ Side ________ Side ________ Top ________ Bottom_______ Surface Area = ________ Volume ______ 5) Front _______ Back________ Side ________ Side ________ Top ________ Bottom_______ Surface Area = ________ Volume ______ Word Problems: 1) Kevin wants to paint the walls and ceiling of room. His room is 11 feet long, 12 feet wide and 8 feet high. How many square feet will he cover? Draw Picture: One gallon of paint will cover 200 ft² of surface area. How many gallons of paint does Kevin need to buy to paint his room? 2) Alisha wants to paint the walls of her bedroom. Her room is 18 feet long, 14 feet wide, and 10 feet high. The paint she decides to buy will cover 100 square feet. How many gallons will she need? Guided Notes – Surface Area and Volume Word Problems Date ______________ Review 2) 1) Volume ____________ Volume ____________ Surface Area _____________ Surface Area _____________ Word Problems: Word problems will not tell you to find the surface area and volume. *How you know: the question is asking for _____________________ if they are talking about the outside of the object. It is asking for __________________________ if the question discusses filling an object. Examples: 1) A company is deciding on the box to use for their cereal. Box A measures 8 inches by 2.25 inches by 10.5 inches. How much material is needed to make box A? 2) Sara wants to paint the walls of her bedroom. Her bedroom is 12 ft long, 8 ft wide and 10 feet high. What is the area of the space she wants to paint? How many cubic inches of cereal can fit in Box A? If the paint costs $6.50 a gallon and each gallon covers 128 ft² of wall, how much will it cost to paint the room? Draw picture: Draw picture: Date ____________ Guided Notes – Surface and Volume of Right Prisms Right Prism: A prism which has 2 _____________ aligned one directly above the other and the rest of its faces are _____________________. Volume Formula = ______________, where B is the _________ of the base *Remember to determine the height as how tall the object is if it stands on its _________ 1) Find the volume of the pentagonal prism if the area of the base is 100 in². 2) Find the volume of the trapezoidal prism if the area of the base is 12 in². 3) Find the volume of the ______________________ prism if the area of the base is 192 in². 45 in Determining the height 4) Find the volume of the triangular prism if the area of the base is 24 in². 5) Find the volume of the trapezoidal prism if the area of the base is 165 in². h = __________ h = __________ V = __________ V = __________ 1) Pictures of Sides: V = _________ SA = _______ 2) V = _________ SA = _______ 3) V = _________ SA = _______ 4) V = _________ SA = _______ 5) V = _________ SA = _______ 6) V = _________ Test Examples: 1) 2) Name_______________________ Surface Area and Volume Levels Level 1: Find the surface area and volume of the following shapes. 1.) 2.) 3.) 5 cm V = ________ V = ________ V = ________ SA = _________ SA = _________ SA = _________ Level 2: 2.) 3.) 1.) V = ________ Level 3: 1.) SA = _________ V = ________ V = ________ 2.) SA = _________ Level 4 1.) Sara wants to paint the walls of her bedroom. Her room is 9 feet long, 12 feet wide, and 10 feet high. How much paint will she need? If each gallon of paint covers 200 square feet, how many gallons will she need? 2.) Jack is going to paint the ceiling and walls of his room. If his room is 14 ft high, 10 feet wide, and 9 feet long, what is the area he has to paint? 2) If each can of paint covers 200 square feet, how many cans of paint does he need? If each gallon of paint costs $15, how much money will Sara spend? Level 5 2.) 1.) V ___________ V ___________ SA _____________ SA _____________ Level 6 Find the surface area of the figures below. Draw out the sides to help you. 1.) Level 7 2.) ADVANCED Surface Area and Volume Levels Level 1 1) 2) Level 2 1) 2) Level 3 1) Level 4 Level 5 2) Bradley cut a square hole of wood in wood shop. If the block was cube-shaped with side lengths of 8 inches, and the hole had the side lengths of 3 inches, how much wood was left after the hole was cut out? Level 6 Level 7 Level 8 Level 9 Level 10 Find the surface area of the figure below. Guided Notes – Geometry Using Algebra To Find Missing Dimensions Date _____________ Dimension: _________________, ______________, or ________________ Together On Your Own 1) 1) A box has a length of 14 cm, a height of 12 cm and a volume of 3,108 cm³. What is the width of the box? What is the surface area of the box? What is the surface area of the picnic cooler? 2) 2) 3) 3) Together On Your Own 4) 5) 4) 5) Guided Notes – Cross Sections Date ___________ Cross Section: A plane that intersects or ___________________ a _____________,forming a two-dimensional figure Your Goal: Be able to identify or draw the _____________________ of the cross section. *Can slice horizontally ________________________ or vertically _____________________ Example 1: A cylinder cut horizontally makes a cross section that is a ______________ Example 3 : A plane cuts the pentagonal prism horizontally. What is the shape of the cross section? Example 5 : A plane cuts the sphere __________________. What is the shape of the cross section? Example 2: A cylinder cut vertically makes a cross section that is a _________________ Example 4: A plane cuts the triangular pyramid horizontally. What is the shape of the cross section? Example 6: A plane cuts the cone_________________. What is the shape of the cross section? Without a picture: 1) A cone is sitting on its base. Sketch a picture below. 2) A rectangular prism is sitting on its base. Sketch a picture below. If the cone is cut horizontally it makes a If the rectangular prism is cut vertically it cross section that is a makes a cross section that is a ______________________. ______________________. *Cross sections can also be parallel or ____________________ to the _____________ of the solid. Example 1: What cross section is formed when a plane intersects a cylinder so that it is parallel to the bases? Example 2: What cross section is formed when a plane intersects a square pyramid so that it is perpendicular to the base? Without a picture: 1) A triangular right prism is cut perpendicular to the base. What is the shape of the cross section? 2) What solid only has triangles for cross sections? Critical Thinking: 1) Describe how the cross section of Earth changes as you go north from the equator. How does it stay the same? Unit – Geometry Guided Notes – Measuring and Naming Angles Date__________ Two rays that share the same ___________________ form an angle. The point where the rays intersect is called the ____________of the angle. The two rays are called the ______________ of the angle. How do we name an angle? ____________________________________________ Example: Types of Angles Drawing: Acute - _______________________________________________________ Obtuse - ______________________________________________________ Right - ________________________________________________________ Straight - ______________________________________________________ Estimating Angles – Examples: 1) ________ Measuring with Protractor: 2) ________ 3) ________ 4) ________ Adjacent Angles: have a common _______________ and a common ___________________ Name Pairs of Adjacent Angles: _______ and _______ _______ and _______ _______ and _______ _______ and _______ _______ and _______ _______ and _______ Vertical Angles: a pair of ____________________________ angles made by intersecting lines Vertical angles are __________________________________. Guided Notes – Angles Date__________ Supplementary: _________________________________________ Example: Angle ______ + Angle _____ = _______° Complementary: _________________________________________ Angle ______ + Angle _____ = ________° To Find a Missing Angle: 1. Determine if the angles are complementary (_____) or supplementary (_____) 2. Write an _____________________________for the missing angle. 3. ___________________________ the equation. Complementary or Supplementary? Find the missing angle. 1) 2) 3) 4) 5) To Find a Missing Angle: Use what you know about vertical angles, adjacent angles, complementary angles and supplementary angles to find the missing angles in the puzzles below. 1) 2) 4) 5) Enrichment – Find the Value of x 1) 2) 3) To Find a Missing Angle: Use what you know about vertical angles, adjacent angles, complementary angles and supplementary angles to find the missing angles in the puzzle below. 1) Guided Notes – Angles of Triangle Date__________ Angles of a Triangle_______________________________________________________ Example: 1) 3) 2) The measure of one angle in a right triangle is 30°. What is the measure of the third angle? Isosceles Triangle _____________________ 4) Stacey drew angles of 55°, 75° and 59°. Could her angles form a triangle? Why or why not? Equilateral Triangle ____________________ Finding Exterior Angles 1) 2) 3) Finding a Variable Find the value of the variable(s) in each of these triangles. 1) 2) 3) CHALLENGE! Unit – Geometry Guided Notes – Types of Triangles All sides congruent ______________________angle Date__________ Two sides congruent All ____________________Angles Examples: Classify the triangle in two ways 1) 2) 4) 3) a. b. c. d. Right isosceles triangle Acute isosceles triangle Obtuse isosceles triangle Obtuse scalene triangle No sides congruent ________________________angle Triangle Side Lengths Date__________ Triangle Inequality Theorem: The sum of any two sides of a triangle is always _______________________ than the third side. 1) Could a triangle have side lengths of: Side 1: 4 Side 2: 8 Side 3: 2 2) Could a triangle have side lengths of: Side 1: 3 Side 2: 4 Side 3: 5 Tests: 1) _______________ 2) _______________ 3) _______________ Tests: 1) _______________ 2) _______________ 3) _______________ 3) 4) Two sides of an isosceles triangle measure 3 and 7. Which of the following could be the measure of the third side ? A. B. C. 5) Is it possible to draw a triangle with a 90˚ angle and one leg that is 4 inches long and one leg that is 3 inches long? If so, draw one. Is there more than one such triangle? 9 7 3 6) Jenna is drawing a blueprint of the stage for the school show. The stage will be in the shape of a triangle. Two sides of the triangle measure 12 and 15 feet respectively. What is the range of the whole-number lengths for the third side of the triangle?