Geometry 3.4 Leavin’ on a Jet Plane

3.4 Area and Perimeter of Trapezoids on the Coordinate Plane Objectives Determine the perimeter and the area of trapezoids and hexagons on a coordinate plane Determine the perimeter of composite figures on the coordinate plane

Problem 1 Well, It’s the Same, But It’s Also Different! On Your Own 1-2 (2 Minutes) Trapezoid A quadrilateral with exactly one pair of parallel sides The parallel sides are called the bases The non-parallel sides are called the legs

Problem 1 Well, It’s the Same, But It’s Also Different! Together 3-5 a. Bases 𝐴𝐷 𝑎𝑛𝑑 𝐵𝐶 𝑎𝑟𝑒 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 b. Legs 𝐴𝐵 𝑎𝑛𝑑 𝐷𝐶 𝑎𝑟𝑒 𝑁𝑂𝑇 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙

Problem 1 Well, It’s the Same, But It’s Also Different! a. Perimeter without Distance Formula Pythagorean Theorem 𝑎 2 + 𝑏 2 = 𝑐 2

Problem 1 Well, It’s the Same, But It’s Also Different! b. Find the Perimeter 𝐴𝐵=8 𝑢𝑛𝑖𝑡𝑠 (𝑉𝑒𝑟𝑡𝑖𝑐𝑎𝑙) 𝐵𝐶=11 𝑢𝑛𝑖𝑡𝑠 (𝐻𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙) 𝐴𝐷=5 𝑢𝑛𝑖𝑡𝑠 (𝐻𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙) 𝑎 2 + 𝑏 2 = 𝐶𝐷 2 8 2 + 6 2 = 𝐶𝐷 2 64+36= 𝐶𝐷 2 𝐶𝐷= 100 =10 𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟=8+11+5+10=34 𝑢𝑛𝑖𝑡𝑠

Problem 2: Using What You Know Area of a Parallelogram: A = bh Base and Height are perpendicular Together #1

Problem 2: Using What You Know d. 𝐴 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑜𝑔𝑟𝑎𝑚 =𝑏ℎ 𝐴= 𝑏 1 + 𝑏 2 ℎ e. 1 2 𝐴= 1 2 𝑏 1 + 𝑏 2 ℎ 𝐴𝑟𝑒𝑎 𝑡𝑟𝑎𝑝𝑒𝑧𝑜𝑖𝑑 = 1 2 𝑏 1 + 𝑏 2 ℎ Together #1

Problem 2: Using What You Know Together #2 The area formula for a trapezoid is one-half the area of a parallelogram because a parallelogram can be divided into two congruent trapezoids

Problem 2: Using What You Know Collaborate 3-4 (4 Minutes) 𝐴= 1 2 𝑏 1 + 𝑏 2 ℎ 𝐴= 1 2 4+7 4 𝐴= 1 2 11 4 𝐴=22 𝑠𝑞𝑢𝑎𝑟𝑒 𝑢𝑛𝑖𝑡𝑠

Skip Problem 3 Same strategy as a parallelogram that had no horizontal or vertical sides. Draw a rectangle around the trapezoid and subtract the triangles

Problem 4: Jets and Trapezoids! Collaborate 1-2 (2 Minutes) Collaborate 3-6 (4 Minutes) It is easier to change the larger unit to the smaller unit We should change miles per hour to miles per minute 600 𝑚𝑖𝑙𝑒𝑠 1 ℎ𝑜𝑢𝑟 𝑥 1 ℎ𝑜𝑢𝑟 60 𝑚𝑖𝑛𝑢𝑡𝑒𝑠 =10 𝑚𝑖𝑙𝑒𝑠 𝑝𝑒𝑟 𝑚𝑖𝑛𝑢𝑡𝑒

Problem 4: Jets and Trapezoids! 600 𝑚𝑖𝑙𝑒𝑠 1 ℎ𝑜𝑢𝑟 𝑥 1 ℎ𝑜𝑢𝑟 60 𝑚𝑖𝑛𝑢𝑡𝑒𝑠 =10 𝑚𝑖𝑙𝑒𝑠 𝑝𝑒𝑟 𝑚𝑖𝑛𝑢𝑡𝑒 𝐴 𝑡𝑟𝑎𝑝𝑒𝑧𝑜𝑖𝑑 = 1 2 25+20 10 𝑇𝑜𝑡𝑎𝑙 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒=225 𝑚𝑖𝑙𝑒𝑠 𝑖𝑛 25 𝑚𝑖𝑛𝑢𝑡𝑒𝑠 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑇𝑟𝑎𝑣𝑒𝑙𝑒𝑑 𝑖𝑛 5 minutes 𝐴 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 = 1 2 5 10 =25 𝑚𝑖𝑙𝑒𝑠

Summary What is the formula for area of a trapezoid? 𝐴= 1 2 𝑏 1 + 𝑏 2 ℎ When using units, which is it easier to convert to? Always change the larger unit to the smaller unit Hours to Minutes Yards to Feet Years to Days Etc.

Formative Assessment Skills Practice 3.4 Pg. 409-412 (1-6)