Beijing Normal University Version Fifth Grade Volume 1 XXX Central Primary School Length * width Side Length * Side Length Bottom * height Bottom * Gao Gao 2 (Rectangular width) The height of the original parallelogram The bottom of the original parallelogram (Rectangular rectangle) 高 底 Two identical triangles can be c ombined into a parallelogram. There Thereisisaacommon commonpoint pointin inthe thederivation derivationof of area areaformulas formulasfor forparallelograms parallelogramsand andtriangl triangl es. es.What Whatisisit? it? conversion conversion Find out the connec Find out the connec tion tion Derived formula Derived formula Upper floor 腰 high map out the course of action beforehan d 腰 There is a dam whose cross section is trapezoidal, the length of the dam top is 20 meters, the length of the dam bottom is 80 meters, and the height of the da m is 40 meters.What is the area of the cross section of the dam? 40 m 20 m 80 m Hands-On Activit ies Tips: 1. What known graphics are you going to conve rt the trapezoids into? 2. What is the relationship between each part of the transformed graph and the top, bottom and height of the trapezoid? 3. My findings: 4. My question: Upper floor (Pairing) high map out the cour se of action befor ehand Two identical trapezoids can be pieced together to form a flat The bottom of a parallelogram corresponds to a trapezium. The height of () is equal to that of trapezoidal (). high Bottom + Bottom Trapezoidal area= (Bottom + Bottom) *Gao 2 Can you answer that? •(Bottom + Bottom) is calculated as follows: Parallelogram of two identical trapezoids Bottom! •(Bottom + Bottom) *High calculates: Parallelogram of two identical trapezoids The measure of area Dividing the area of a parallelogram by two is a trapezoid. The measure of area (Cut-and-fill metho d) Upper floor (1) Bottom x Gao_2 high Upper Bottom * Gaoyu 2 II. map out the course of action beforehand Trapezoidal area= = Upper Bottom * Gaoyu 2 + (Bottom + Bottom) Bottom x Gao_2 * Gao Gao 2 (Cut-and-fill method) The bottom of the assembled parallelogram is equivalent to a ladder. Of or equal to a trapezoid in height. Bottom + Bottom High (). half There is a dam whose cross section is trapezoidal, the length of the dam top is 20 meters, the length of the dam bottom is 80 meters, and the height of the da m is 40 meters.What is the area of the cross section of the dam? S ladder= (a + b) h_2 (20+80)*40 2 =4000 2 40 m = 100 x 40 2 20 m = 2000 (square meters) Answer: The cross-sectional area of the dam is 2000 square meters. 80 m Standard Practice 1. Calculate the area of each trapezoid below.(Unit: c m) 5 8 10 20 8 11 12 8 10 S=(a+b)*h_2 S=(a+b)*h_2 S=(a+b)*h_2 = (5+10)*8 2 = (8+12)*10 2 = (8+20)*11 2 = 60 (square centimete= 100 (square centimete = 154 (square centimet r) r) r) 2. The top and bottom of a trapezoid is 9 cm, 3 cm s horter and 10 cm higher than the bottom. What's its area ? B = 9 + 3 = 12 (cm) S=(a+b)*h_2 = (9+12)*10 2 = 21 x 10 2 = 105 (square centimeter) Answer: The trapezoidal area is 105 square centimeters. 3. We often see piles of logs, steel tubes and other shapes under imaging. Question: Comprehensive exerc ises 1. The area of a parallelogram is twice that of a trapezoid.() X 2. Two trapezoids must be able to form a parallelogram.() X 3. Two trapezoids of equal base and equal height can be combined into a flat one. X Line quadrilateral.() X 4. Two trapezoids of equal area must be equal base and equal height.() 2 4 10 5 8 16 2. Compare the following trapezoidal areas. W hat did you find? 2cm 1cm 7cm 3cm 6cm 7cm 8cm Think, draw, cut 1. Cut only one knife and cut the trapezoid into a triangle and a trapezoid. 2. Cut only one knife and cut the trapezoid into a parallelogram and a trapezoid. 3. Cut only one knife and cut the trapezoid into two trapezoids. 4. Cut only one knife and cut the trapezoid into two triangles. (1) (2) (3) (4)