CC Geometry H Aim #9: How do we find perimeter and area of polygonal regions defined by systems of inequalities in the coordinate plane? Do Now: Graph the following: a) b) 1) A parallelogram with base of length b and height h can be situated in the coordinate plane as shown. a) Find the coordinates of the vertices: D C A________ B _______ C ________ D _________ b) Verify that the shoelace formula gives the area of the parallelogram as bh. A B 2) A triangle with base of length b and height h can be situated in the coordinate plane as shown. a) Find the coordinates of the vertices: C A________ B _______ C ________ b) Verify that the shoelace formula (Green's theorem) gives the area of the triangle as (1/2)bh. A B 3) A quadrilateral region is defined by the system of inequalities below: y ≤ x + 6 y ≤ -2x + 12 y ≥ 2x - 4 y ≥ -x + 2 a. Sketch the region. b. Determine the vertices of the quadrilateral. How can you verify the intersection points? c. Find the perimeter of the quadrilateral region to the nearest hundredth. d. Find the area of the quadrilateral region. 4) A quadrilateral region is defined by the system of inequalities below: y ≤ x + 5 y ≥ x - 4 y ≤ 4 y ≥ a. Sketch the region. y ≤ x + 5 b. Determine the vertices of the quadrilateral. A(­1,4) B(­4,1) C(0,­4) D(8,4) A y ≤ 4 D c. Find the perimeter of the quadrilateral B region to the nearest hundredth. P ≈ 30.96 units y ≥ x - 4 d. Find the area of the quadrilateral region. C A = 49.5 units2 y ≥ 5) a. Sketch the region. b. Determine the coordinates of the vertices. c. Find the perimeter of the region to the nearest hundredth. d. Find the area of the region. 8x - 9y ≥ -22 x + y ≤ 10 5x - 12y ≤ -1 Name____________________ CC Geometry H Date _____________ HW #9 1) A quadrilateral region is defined by the system of inequalities below: y ≤ 5 y ≤ 2x + 1 y ≥ -3 y ≥ 2x - 7 a. Sketch the region. b. Determine the vertices of the quadrilateral. c. Find the area of the quadrilateral region. 2) Identify the system of inequalities that defines the region shown: a) y b) y x x 3) a. Sketch the region. b. Determine the coordinates of the vertices. c. Find the perimeter of the region to the nearest hundredth. d. Find the area of the region. x + 3y ≥ 0 4x - 3y ≥ 0 2x + y ≤ 10 Review: 1) Complete a two-column proof: Given: ΔABC and ΔEDC, C is the midpoint of BD and AE Prove: AB || DE A B C D E.