Day 116 Bellringer 1. Use the triangle below to answer the questions that follow. 3 in 5 in 4 in a) Find the area of the triangle. b) Find the perimeter of the triangle. 2. Use the distance formula to find the distance beween each set of points given below. a) A(2,3) and B(4,6) b) B(4,6) and C( 2, 3) c) D(4,5) and E(2,1) HighSchoolMathTeachers@2017 Page 1
Day 116 Bellringer Answer Key Day 116: 1. a) 6 in 2 b) 12 in 2. a) 13 units b) 3 13 units c)2 5 units HighSchoolMathTeachers@2017 Page 2
Day 116 Activity 1. On the grid provided below, draw a triangle with vertices at F( 4 3), G(4, 3) and H(4,3) y 4 2-6 -4-2 0 2 4 6 x -2-4 2. Using the distance formula, find the length of FG. 3. Using the distance formula, find the length of GH. 4. Taking FG as the base and GH as the height, find the area of FGH. 5. Using the formula, A = 1 2 (x 1(y 2 y 3 ) + x 2 (y 3 y 1 ) + x 3 (y 1 y 2 )), find the area of FGH. Do you get the same area with the two different methods? HighSchoolMathTeachers@2017 Page 3
Day 116 Activity In this activity students will draw a triangle on xy- plane and use different ways to find its area. Students will work in groups of at least three and each is required to have a pencil and a ruler. Answer Keys Day 116: 1. y 4 H 2-6 -4-2 0 2 4 6 x -2 F G -4 2. 8 units 3. 6 units 4. 24 sq. units 5. 24 sq. units Yes. HighSchoolMathTeachers@2017 Page 4
Day 116 Practice A triangle has its vertices at points S(1,0), T(6,1) and U(1,4). 1. Find the length of ST. 2.Find the length of TU. 3. Find the length of US. 4. Find the perimeter of STU. 5. Find the area of STU. A triangle has its vertices at points M( 6, 2), N( 6, 10) and O(0, 2). 6.Find the length of MN. 7.Find the length of NO. 8.Find the length of OM. 9.Find the perimeter of MNO. 10. Calculate the area of MNO. A triangle has its vertices at points J( 1, 1), K( 1,5) and L( 4,2). 11. Find the length of JK. 12.Find the length of KL. 13.Find the length of LJ. HighSchoolMathTeachers@2017 Page 5
Day 116 Practice 14.Determine the perimeter of JKL. 15.Find the area of JKL. QPR has vertices Q(1, 3), P(3, 4) and R(3, 1). 16.Find the length of QP. 17.Find the length of PR. 18.Find the length of RQ. 19.Find the perimeter of QPR. 20.Find the area of QPR. HighSchoolMathTeachers@2017 Page 6
Day 116 Practice Answer Keys Day 116: 1. 26 units 2. 34 units 3. 4 units 4. (4 + 26 + 34) units or 14.93 units 5. 10 sq. units 6. 8 units 7. 10 units 8. 6 units 9. 24 units 10. 24 sq. units 11. 4 units 12. 5 units 13. 10 units 14. (9 + 10) units 15. 6 sq. units 16. 5 17. 3 18. 2 2 19. 3 + 2 2 + 5 units 20. 3 sq. units HighSchoolMathTeachers@2017 Page 7
Day 116 Exit Slip Find the area of a triangle with its vertices at points A( 1,3), B(2,3) and C( 1, 1). HighSchoolMathTeachers@2017 Page 8
Day 116 Exit Slip Answer Keys Day 116: 6 in 2 HighSchoolMathTeachers@2017 Page 9
Day 117 Bellringer 1. Calculate the perimeter of the following quadrilaterals (not drawn to scale) whose dimensions are given in inches. (a) 15.5 4.4 (b) 7.6 7.6 2. Find the area of each of the quadrilaterals described below: (a) A rectangle whose length is 30.2 feet and breadth is 17.9 feet. (b) A square whose side is 60.6 inches 3. Find the distance BD given that the coordinates of B and D are ( 1, 7) and (11, 8) respectively. Leave your answer in radical form. HighSchoolMathTeachers@2017 Page 10
Day 117 Bellringer Answer keys Day 117: 1. (a) 39.8 inches (b) 30.4 inches 2. (a) 540.58 square feet (b) 3672.36 square inches 3. 3 41 units. HighSchoolMathTeachers@2017 Page 11
Day 117 Activity 1. On the graph paper provided plot the points P(0, 3), Q(4, 0), R(1, 4) and S( 3, 1) 2. Join the points to form the vertices of quadrilateral PQRS. 3. Use the distance formula to calculate the length of side PQ. 4. Use the distance formula to calculate the length of side QR. 5. Use the distance formula to calculate the length of side RS. 6. Use the distance formula to calculate the length of side PS. 7. What do you notice about the lengths of the sides you have calculated in 3 to 6 above? 8. Through careful observation of the quadrilateral and basing on your response to 7 above, which type of quadrilateral have you just drawn? 9. Use the side lengths you have calculated to find the perimeter of quadrilateral PQRS. 10. Use the side lengths you have calculated to find the area of quadrilateral PQRS. HighSchoolMathTeachers@2017 Page 12
Day 117 Activity In this activity students will work in groups of three or four to calculate the area of a square on the coordinate plane. The students will require a graph paper and a ruler. Answer keys Day 117: 1. y 6 4 R 2 S Q -4-2 2 4 6 8-2 P x 2. The points should be joined in the appropriate order 3. 5 units 4. 5 units 5. 5 units 6. 5 units 7. All the sides are congruent 8. A square 9. 20 units 10. 25 square unit HighSchoolMathTeachers@2017 Page 13
Day 117 Practice Square WXYZ has vertices W(2, 1), X(2, 1), Y(4, 1) and Z(4, 1). Use this information to answer questions 1-5. 1. Find the length WX. 2. Find the length XY 3. Find the length YZ 4. Find the length WZ 5. Determine the perimeter of square WXYZ 6. Determine the area of square WXYZ Rectangle JKLM has vertices J( 1, 2), K( 1, 2), L(1, 2) and M(1, 2). Use this information to answer questions 7-12. 7. Find the length JK. 8. Find the length KL 9. Find the length LM HighSchoolMathTeachers@2017 Page 14
Day 117 Practice 10. Find the length JM 11. Determine the perimeter of rectangle JKLM 12. Determine the area of rectangle JKLM Rectangle QRST is drawn on a grid with coordinates Q( 2, 2), R( 2, 2), S(1, 2) and T(1, 2). Use this information to answer questions 13-18. 13. Calculate the length of side QR. 14. Calculate the length of side RS 15. Calculate the length of side ST. 16. Calculate the length of side QT 17. Determine the perimeter of rectangle QRST 18. Determine the area of rectangle QRST HighSchoolMathTeachers@2017 Page 15
Day 117 Practice Use the grid below to answer questions 19 and 20. x 4 3 D C 2 1 A B 0 1 2 3 4 5 6 y 19. Find the perimeter of rectangle ABCD above. 20. Determine the area of rectangle ABCD above. HighSchoolMathTeachers@2017 Page 16
Day 117 Practice Answer keys Day 117: 1. 2 units 2. 2 units 3. 2 units 4. 2 units 5. 8 units 6. 4 sq. units 7. 4 units 8. 2 units 9. 4 units 10. 2 units 11. 12 units 12. 8 sq. units 13. 4 units 14. 3 units 15. 4 units 16. 3 units 17. 14 units 18. 12 units 19. 10 units 20. 6 sq. units HighSchoolMathTeachers@2017 Page 17
Day 117 Exit Slip The coordinates of the vertices of a quadrilateral are K( 4, 4), L( 4, 1), M(5, 1) and N(5, 4), find its perimeter and area. HighSchoolMathTeachers@2017 Page 18
Day 117 Exit Slip Answer keys Day 117: Perimeter = 24 units Area = 27 sq. units HighSchoolMathTeachers@2017 Page 19
Day 116 Bellringer 1. Find the perimeter of the each of the quadrilaterals described below: (a) A rhombus whose side has a length of 11.4 inches. (b) A parallelogram which measures 22.7 feet by 13.4 feet. 2. A rhombus has an area of 2 400 square inches. Given that the rhombus has a perimeter of 240 inches, calculate the altitude of the rhombus. 3. Find the area of the each of the quadrilaterals described below: (a) A rhombus of height 12.4 inches whose side has a length of 28.4 inches (b) A parallelogram whose length and altitude are 45.8 feet and 26.8 feet respectively. HighSchoolMathTeachers@2017 Page 20
Day 116 Bellringer Answer keys: Day 118: 1. (a) 45.6 inches (b) 72.2 inches 2. 40 inches 3. (a) 352.16 square inches (b) 1227.44 square feet HighSchoolMathTeachers@2017 Page 21
Day 118 Activity 1. On the graph paper provided plot the points P(1, 1), Q(5, 3), R(7, 7) and S(3, 5) 2. Join the points to form the vertices of rhombus PQRS. 3. Use the distance formula to calculate the length of side PQ. 4. Use the distance formula to calculate the length of side QR. 5. Use the distance formula to calculate the length of side RS. 6. Use the distance formula to calculate the length of side PS. 7. Use the distance formula to calculate the length of side QS. 8. Use a ruler to draw a broken line from vertex Q to vertex S. 9. Name the two triangles that are formed inside quadrilateral PQRS that share line line in 8 above.. 10. Use Heron s formula to find the area of each triangles in 9 above. 11. Find the area of the rhombus PQRS by finding the sum of the two triangles that make it up. HighSchoolMathTeachers@2017 Page 22
Day 118 Activity In this activity students will work in groups of four to calculate the area of a rhombus on the coordinate plane. The students will require a graph paper and a ruler. Answer keys Day 118: 1. Graph should appropriately plotted y 8 R 6 S 4 2 Q P 6 2. No response 3. 20 = 4.472 units 4. 20 = 4.472 units 5. 20 = 4.472 units 6. 20 = 4.472 units 7. 8 = 2.828 units 2 4 6 8 10 12 8. No response 9. PQS and RQS 10. Area of PQS = 6 sq. units and Area of RQS = 6 sq. units 11. 12 sq. units x HighSchoolMathTeachers@2017 Page 23
Day 118 Practice Quadrilateral WXYZ has vertices W( 10, 2), X( 8, 6), Y( 6, 2) and Z( 8, 2). Use this information to answer questions 1-7. Leave your answer in radical form where possible. 1. Find the length WX. 2. Find the length XY 3. Find the length YZ 4. Find the length WZ 5. Find the perimeter of WXYZ. 6. Find the length WY 7. Draw the figure on the xy-plane and find the area of one of the triangles formed when segment WY is drawn. 8. Hence find the area of the quadrilateral. HighSchoolMathTeachers@2017 Page 24
Day 118 Practice Quadrilateral JKLM has vertices J(3, 2), K(8, 2), L(11, 6) and M(6, 6). Use this information to answer questions 9-16. 9. Find the length JK. 10. Find the length KL 11. Find the length LM 12. Find the length JM 13. Determine the perimeter of the figure. 14. Find the length KM 15. Draw the figure on the xy-plane figure and find the area of one of the triangles formed when figure JKLM is divided into two by segment KM. 16. Hence find the area of the rhombus. HighSchoolMathTeachers@2017 Page 25
Day 118 Practice Use the grid below to answer questions 17-20. y 4 3 D C 2 1 A B 1 2 3 4 5 6 x 17. Calculate the length of side AB and BC. 18. Calculate the length of side BD 19. Determine the perimeter of parallelogram ABCD. 20. Calculate the area of parallelogram ABCD. HighSchoolMathTeachers@2017 Page 26
Day 118 Practice Answer keys Day 118: 1. 2 5 units 2. 2 5 units 3. 2 5 units 4. 2 5 units 5. 8 5 units 6. 4 units 7. 8 sq. units each y Z 4 2-10 -8-6 -4-2 2 4 6 8 x W Y -2-4 X -6-8 8. 16 sq. units 9. 5 units 10. 5 units 11. 5 units 12. 5 units 13. 20 units 14. 2 5 units HighSchoolMathTeachers@2017 Page 27
Day 118 Practice 15. 10 sq. units each 16. 20 sq. units y 8 6 M L 4 2 J K 6 2 4 6 8 10 12 x 17.AB = 3 units; BC = 5 units 18. BD = 2 2 units 19. 6 + 2 5 units 20. 6 sq. units HighSchoolMathTeachers@2017 Page 28
Day 118 Exit Slip The coordinates of the vertices of parallelogram KLMN are: K( 4, 4), L( 1, 1), M(5, 1) and N(2, 4). Calculate the area of parallelogram KLMN. HighSchoolMathTeachers@2017 Page 29
Day 118 Exit Slip Answer keys Day 118: 18 square units HighSchoolMathTeachers@2017 Page 30
Day 119 Bellringer 1. Identify a trapezoid(s) from the following diagrams (i) (ii) (iii) (iv) (v) 2. Find the slope of the line passing through ( 3,2) and (1, 6). Determine the distance between the points in 3 and 4 below. 3.(3,4) and ( 4, 3). 4. (4, 5) and ( 1, 1). 5. Find the area of the following trapezoid. 8 in 6 in 15 in 30 HighSchoolMathTeachers@2017 Page 31
Day 119 Bellringer Answer Key Day 119: 1. (ii) and (v) 2. -2 3. 7 2 units 4. 41 units 5. 34.5 sq. units4 HighSchoolMathTeachers@2017 Page 32
Day 119 Activity 1.On the grid provided below, note that the line segment PQ is part of a trapezoid. y 4 2 Q -6-4 -2 0 2 4 6 x -2 P -4 2.Draw any line segment not equal to PQ but parallel and above it. 3.Connect its end points to P and Q, to have a trapezoid. 4.What are the coordinates of the points that marks the vertices of the trapezoid? 5.Find the distance of the lengths (provide the exact values). 6. Compute the perimeter of the trapezoid (provide the exact values). 7. Identify the perpendicular height of the trapezoid. Why do ou think it is a perpendicular height? 8. Compute the area of the trapezoid. HighSchoolMathTeachers@2017 Page 33
Day 119 Activity In this activity students will draw a trapezoid on xy- plane and a use the distance formula to determine their length and consequently, compute the area and the perimeter. Students will work in groups of at least three and each group is required to have pencil, a graph paper and a ruler. Answer Keys Day 119: 1-3. No response 4. Different responses 5 6. Different responses, Answer must have roots 7. Different lines segments can be identified but they must be parallel. Reason, the product of its slope and that of one parallel line is -1. 8. Different responses, Answer must have roots HighSchoolMathTeachers@2017 Page 34
Day 119 Practice Use the figure below to answer questions 1-12 (Give exact values in all questions) PLMN is a trapezoid with the perpendicular height LG where the coordinates of the points are P( 4, 1), L(0, 3), M(8,5), N(6,9) and G( 3,0). LM and PN are parallel lines. The trapezoid respresents a map of a piece of a land drawn to a scale of 1 in represents 3600 2 in. 1. Show that LM and PN are parallel lines. 2. Show that LG is the perpendicular height of the trapezoid. 3. Find the length of the perpendicular height. 4. What is the length of the side PL and NM. 5. What is the length of side LM and PN. 6. Is the trapezoid an Isosceles trapezium? Explain your answer. 7. Find the area of the trapezoid on xy-plane. 8. Find the perimeter of the trapezoid on xy-plane. 9. Find the actual measurements of the trapezoid. 10. Find the actual distance around the peiece of land. HighSchoolMathTeachers@2017 Page 35
Day 119 Practice 11. Find the actual area of the piece of land. 12. The piece of land is to be faced with barbed wire whose support poles are to be erected at a uniform distance of 36 in from each other. Find the approximate number of poles that are used? Use the following diagram to answer the following questions. 13 17. Give exact values only as answers. y M 4 3 L 2 1 P -3-2 -1 1 2 3 4 5 6 x S -1-2 13. Find the length of MS and LP 14. Find the length of SP and ML. 15. Determine the length of the perpendicular height. 16.Compute the area of the trapezoid. 17. Compute the perimeter of the trapezoid. HighSchoolMathTeachers@2017 Page 36
Day 119 Practice Use the following diagram to answer the following questions. 18 20. Give exact values only as answers. F y 4 3 2 1 Q -3-2 -1 1 2 3 Y 4 5 6 x -1-2 A 18. Determine the length of the perpendicular height. 19. Determine the lengths of the smaller and the larger parallel line segments. 20. Determine the area of the trapezoid. HighSchoolMathTeachers@2017 Page 37
Day 119 Practice Answer Keys Day 119: 1. Slope of LM = 1 = Slope of PN 2. Slope of LG( 1) slope of LM(1) = -1 3. 3 2 4. PL = 2 5 in, NM = 2 5 in 5. PN = 10 2 in, LM = 8 2 in 6. Yes, Non parallel opposite sides PL and NM are equal 7. 54 sq. in 8. 18 2 + 4 5 in 9. PL = 7200 10 in, NM = 7200 10 in PN = 72000 in, LM = 57600 in in 10. 129600 + 14400 10 in 11. 194400 2 sq. in 12. 4000 13. MS = 5 units, LP = 2 units 14. SP = 29 units, ML = 26 units 15. 5 units 16. 17.5 sq. units 17. (7 + 29 + 26)units 18. 2 2 units 19. Smaller line segment = 2 2 units Larger line segment = 4 2 units 20. 12 sq.in HighSchoolMathTeachers@2017 Page 38
Day 119 Exit Slip How would you identify an perpendicular height of a trapezoid on an xy plane HighSchoolMathTeachers@2017 Page 39
Day 119 Exit Slip Answer Keys Day 119: Find the slope of one of the parallel lines of the trapezoid and that of the side or a line that you purpote to be perpendicular height. If the product of their slope is -1, then the line is the perpendicular height. HighSchoolMathTeachers@2017 Page 40