Name Date Chapter Fair Game Review Find the area of the square or rectangle... ft cm 0 ft cm.. in. d in. d. Find the area of the patio. ft 0 ft Copright Big Ideas Learning, LLC Big Ideas Math Green
Name Date Chapter Fair Game Review (continued) Plot the ordered pair in a coordinate plane.. (, ). (, ) x x. (, ) 9. (, ) x x 0. (, ). (, ) x x Big Ideas Math Green Copright Big Ideas Learning, LLC
Name Date. Areas of Parallelograms For use with Activit. Essential Question How can ou derive a formula for the area of a parallelogram? A polgon is a closed figure in a plane that is made up of three or more line segments that intersect onl at their endpoints. Several examples of polgons are parallelograms, triangles, and trapezoids. The formulas for the areas of polgons can be derived from one area formula, the area of a rectangle. Recall that the area of a rectangle is the product of its length and its width w. The process ou use to derive these other formulas is called deductive reasoning. Area = w w Rectangle Parallelogram Triangle Trapezoid Defined Derive Derive Derive Formula Formula Formula Lesson. Lesson. Lesson. ACTIVITY: Deriving the Area Formula of a Parallelogram Work with a partner. a. Draw an rectangle on a piece of grid paper. An example is shown. Label the length and width. Then find the area of our rectangle. width = w A = right angle length = b. Cut our rectangle into two pieces to form a parallelogram. Compare the area of the rectangle with the area of the parallelogram. What do ou notice? Use our results to write a formula for the area A of a parallelogram. Copright Big Ideas Learning, LLC Big Ideas Math Green
Name Date. Areas of Parallelograms (continued) ACTIVITY: Finding the Areas of Parallelograms Work with a partner. A B E C D a. Find the area of each parallelogram b cutting it into two pieces to form a rectangle.* b. Use the formula ou wrote in Activit to find the area of each parallelogram. Compare our answers to those in part (a). c. Count unit squares for each parallelogram to check our results. *Cut-outs are available in the back of the. Big Ideas Math Green Copright Big Ideas Learning, LLC
Name Date. Areas of Parallelograms (continued) What Is Your Answer?. IN YOUR OWN WORDS How can ou derive a formula for the area of a parallelogram?. REASONING The areas of a rectangle and a parallelogram are equal. The length of the rectangle is equal to the base of the parallelogram. What can ou sa about the width of the rectangle and the height of the parallelogram? Draw a diagram to support our answer.. What is the height of the parallelogram shown? How do ou know? Copright Big Ideas Learning, LLC Big Ideas Math Green 9
Name Date. Practice For use after Lesson. Find the area of the parallelogram... in. cm in. cm Find the area of the shaded region... m ft m ft m ft m 0 ft. A stained glass window has an area of 900 square inches. a. One window design is made of rectangular stained glass pieces that are inches b inches. How man stained glass pieces are used in the window? b. Another window design is made of square stained glass pieces that are inches b inches. How man stained glass pieces are used in the window? 0 Big Ideas Math Green Copright Big Ideas Learning, LLC
Name Date. Areas of Triangles For use with Activit. Essential Question How can ou derive a formula for the area of a triangle? ACTIVITY: Deriving the Area Formula of a Triangle Work with a partner. a. Draw an rectangle on a piece of grid paper. Label the length and width. Then find the area of our rectangle. b. Draw a diagonal from one corner of our rectangle to the opposite corner. Cut along the diagonal. Compare the area of the rectangle with the area of the two pieces ou cut. What do ou notice? Use our results to write a formula for the area A of a triangle. Area = Formula ACTIVITY: Deriving the Area Formula of a Triangle Work with a partner. a. Fold a piece of grid paper in half. Draw a triangle so that its base lies on one of the horizontal lines of the paper. Do not use a right triangle. Label the height and the base inside the triangle. b. Estimate the area of our triangle b counting unit squares. Area Estimate b fold h c. Cut out the triangle so that ou end up with two identical triangles. Form a quadrilateral whose area ou know. What tpe of quadrilateral is it? Explain how ou know it is this tpe. d. Use our results to write a formula for the area of a triangle. Then use our formula to find the exact are of our triangle. Compare this area with our estimate in part (b). Area Area = Formula = Exact Area Copright Big Ideas Learning, LLC Big Ideas Math Green
Name Date. Areas of Triangles (continued) ACTIVITY: Estimating and Finding the Area of a Triangle Work with a partner. Each grid square represents square centimeter. Use estimation to match each triangle with its area. Then check our work b finding the exact area of each triangle. Estimate Exact Area Match Match a. cm A b. 0 cm B c. 9 cm C D E d. cm e. 0 cm F G H f. cm Not drawn to scale g. cm h. cm Big Ideas Math Green Copright Big Ideas Learning, LLC
Name Date. Areas of Triangles (continued) What Is Your Answer?. PARTNER ACTIVITY Use the centimeter grid paper to create our own triangle matching activit. Trade with our partner and solve each other s matching activit.. IN YOUR OWN WORDS How can ou derive a formula for the area of a triangle? Copright Big Ideas Learning, LLC Big Ideas Math Green
Name Date. Practice For use after Lesson. Find the area of the triangle... in. ft 0 in. ft.. cm m m 9 cm.. d d mm mm. A triangular bookend has a base of inches and a height of inches. Find the area of the bookend. Big Ideas Math Green Copright Big Ideas Learning, LLC
Name Date. Areas of Trapezoids For use with Activit. Essential Question How can ou derive a formula for the area of a trapezoid? ACTIVITY: Deriving the Area Formula of a Trapezoid Work with a partner. Use a piece of centimeter grid paper. a. Draw an trapezoid so that its base lies on one of the horizontal lines of the paper. b. Estimate the area of our trapezoid (in square centimeters) b counting unit squares. b h Area Estimate b c. Label the height and the bases inside the trapezoid. right angle d. Cut out the trapezoid. Mark the midpoint of the side opposite the height. Draw a line from the midpoint to the opposite upper vertex. e. Cut along the line. You will end up with a triangle and a quadrilateral. Arrange these two figures to form a figure whose area ou know. f. Use our result to write a formula for the area of a trapezoid. b b h Area = Formula g. Use our formula to find the area of our trapezoid (in square centimeters). Area = Exact Area h. Compare this area with our estimate in part (b). Copright Big Ideas Learning, LLC Big Ideas Math Green
Name Date. Areas of Trapezoids (continued) ACTIVITY: Writing a Math Lesson Work with a partner. Use our results from Activit to write a lesson on finding the area of a trapezoid. Area of a Trapezoid Ke Idea Use the following steps to find the area of a trapezoid.... Describe steps ou can use to find the area of a trapezoid. Examples Write examples for finding the area of a trapezoid. Include a drawing for each. a. b. Exercises Write exercises for finding the area of a trapezoid. Include an answer sheet. Find the area... Big Ideas Math Green Copright Big Ideas Learning, LLC
Name Date. Areas of Trapezoids (continued) What Is Your Answer?. IN YOUR OWN WORDS How can ou derive a formula for the area of a trapezoid?. In this chapter, ou used deductive reasoning to derive new area formulas from area formulas ou have alread learned. Describe a real-life career in which deductive reasoning is important. Copright Big Ideas Learning, LLC Big Ideas Math Green
Name Date. Practice For use after Lesson. Find the area of the trapezoid.. m. m m ft 9 ft ft Find the area of the trapezoid with height h and bases band b.. h = 0 d. h = 9 cm b b = d = d b b =. cm =. cm. The triangle and the trapezoid have the same area. Base b is twice the length of base b. What are the lengths of the bases of the trapezoid? b cm cm cm b Big Ideas Math Green Copright Big Ideas Learning, LLC
Name Date Extension. Practice For use after Extension. Find the area of the shaded figure..... Copright Big Ideas Learning, LLC Big Ideas Math Green 9
Name Date Extension. Practice (continued) Find the area of the figure... m cm m cm cm m m. ft. in. ft in. in. ft ft in. in. ft 9. You add a -foot-b--foot section of land to a -foot-b--foot garden. Find the area of the new garden. 90 Big Ideas Math Green Copright Big Ideas Learning, LLC
Name Date. Polgons in the Coordinate Plane For use with Activit. Essential Question How can ou find the lengths of line segments in a coordinate plane? ACTIVITY: Finding Distances on a Map Work with a partner. The coordinate grid shows a portion of a cit. Each square on the grid represents one square mile. a. A public librar is located at (, ). Cit Hall is located at (, ). Plot and label these points. b. How far is the public librar from Cit Hall? c. A stadium is located miles from the public librar. Give the coordinates of several possible locations of the stadium. Justif our answers b graphing. 0 9 0 0 9 0 x d. Connect the three locations of the public librar, Cit Hall, and the stadium using our answers in part (c). What shapes are formed? ACTIVITY: Graphing Polgons Work with a partner. Plot and label each set of points in the coordinate plane. Then connect each set of points to form a polgon. Rectangle: A(, ), B(, 0 ), C(, 0 ), D (, ) Triangle: E(, ), F(, ), G (, ) 0 9 0 0 9 0 x Copright Big Ideas Learning, LLC Big Ideas Math Green 9
Name Date. Polgons in the Coordinate Plane (continued) ACTIVITY: Finding Distances in a Coordinate Plane Work with a partner. a. Find the length of each horizontal line segment in Activit. b. STRUCTURE What relationship do ou notice between the lengths of the line segments in part (a) and the coordinates of their endpoints? Explain. c. Find the length of each vertical line segment in Activit. d. STRUCTURE What relationship do ou notice between the lengths of the line segments in part (c) and the coordinates of their endpoints? Explain. e. Plot and label the points below in the coordinate plane. Then connect each pair of points with a line segment. Use the relationships ou discovered in parts (b) and (d) above to find the length of each line segment. Show our work. S(, ) and T (, ) U( 9, ) and V ( 9, 0) W( 0, ) and X ( 0, 0) Y(, 9 ) and Z (, 9) 0 9 0 0 9 0 x f. Check our answers in part (e) b counting grid lines. 9 Big Ideas Math Green Copright Big Ideas Learning, LLC
Name Date. Polgons in the Coordinate Plane (continued) What Is Your Answer?. IN YOUR OWN WORDS How can ou find the lengths of line segments in a coordinate plane? Give examples to support our explanation.. Do the methods ou used in Activit work for diagonal line segments? Explain wh or wh not.. Use the Internet or some other reference to find an example of how finding distances in a coordinate plane is helpful in each of the following careers. a. Archaeologist b. Surveor c. Pilot Copright Big Ideas Learning, LLC Big Ideas Math Green 9
Name Date. Practice For use after Lesson. Plot and label each pair of points in the coordinate plane. Find the area of the polgon.. A(, ), B(, ), C(, ). D(, ), E(, ), F(, ), G(, ) x x. H(, ), I(, ), J(, ), K(, ). L(, ), M(, ), N(, ), O(, ) x x. The vertices of a sandbox are P(, ), Q(, ), R(, ), and S(, ). The coordinates are measured in feet. What is the perimeter of the sandbox? 9 Big Ideas Math Green Copright Big Ideas Learning, LLC