NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 11 M4 GEOMETRY
Lesson 11: Perimeters and Areas of Polygonal Regions Defined by Systems of Inequalities
Classwork Opening Exercise Graph the following:
a. 7 b. > 3
π¦π¦ β€ π₯π₯ β
1 2 < 4 + 5 c. 2 d. 3
π¦π¦ π₯π₯ β π¦π¦ β₯ β π₯π₯
Lesson 11: Perimeters and Areas of Polygonal Regions Defined by Systems of Inequalities S.49 Date: 10/22/14 This work is licensed under a Β© 2014 Common Core, Inc. Some rights reserved. commoncore.org Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 11 M4 GEOMETRY
Example 1
A parallelogram with base of length and height can be situated in the coordinate plane as shown. Verify that the shoelace formula gives the area of the parallelogram as . ππ β ππβ
Example 2
A triangle with base and height can be situated in the coordinate plane as shown. According to Greenβs theorem, what is the area of the triangle? ππ β
Lesson 11: Perimeters and Areas of Polygonal Regions Defined by Systems of Inequalities S.50 Date: 10/22/14 This work is licensed under a Β© 2014 Common Core, Inc. Some rights reserved. commoncore.org Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 11 M4 GEOMETRY
Exercises 1β2 1. A quadrilateral region is defined by the system of inequalities below: + 6 2 + 12 2 4 + 2
a. Sketchπ¦π¦ β€ theπ₯π₯ region. π¦π¦ β€ β π₯π₯ π¦π¦ β₯ π₯π₯ β π¦π¦ β₯ βπ₯π₯
b. Determine the vertices of the quadrilateral.
c. Find the perimeter of the quadrilateral region.
d. Find the area of the quadrilateral region.
2. A quadrilateral region is defined by the system of inequalities below:
+ 5 4 4 4 5 a. Sketchπ¦π¦ β€ theπ₯π₯ region. π¦π¦ β₯ π₯π₯ β π¦π¦ β€ π¦π¦ β₯ β 4 π₯π₯ β
b. Determine the vertices of the quadrilateral.
c. Which quadrilateral is defined by these inequalities? How can you prove your conclusion?
d. Find the perimeter of the quadrilateral region.
e. Find the area of the quadrilateral region.
Lesson 11: Perimeters and Areas of Polygonal Regions Defined by Systems of Inequalities S.51 Date: 10/22/14 This work is licensed under a Β© 2014 Common Core, Inc. Some rights reserved. commoncore.org Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 11 M4 GEOMETRY
Problem Set
For Problems 1β2 below, identify the system of inequalities that defines the region shown. 1.
2.
For Problems 3β5 below, a triangular or quadrilateral region is defined by the system of inequalities listed. a. Sketch the region. b. Determine the coordinates of the vertices. c. Find the perimeter of the region rounded to the nearest hundredth if necessary. d. Find the area of the region rounded to the nearest tenth if necessary.
3. 8 9 22 + 10 5 12 1
π₯π₯ β π¦π¦ β₯ β π₯π₯ π¦π¦ β€ π₯π₯ β π¦π¦ β€ β 4. + 3 0 4 3 0 2 + 10
π₯π₯ π¦π¦ β₯ π₯π₯ β π¦π¦ β₯ π₯π₯ π¦π¦ β€ 5. 2 5 14 3 + 2 17 2 9 + 0
π₯π₯ β π¦π¦ β₯ β π₯π₯ π¦π¦ β€ π₯π₯ β π¦π¦ β€ π₯π₯ π¦π¦ β₯
Lesson 11: Perimeters and Areas of Polygonal Regions Defined by Systems of Inequalities S.52 Date: 10/22/14 This work is licensed under a Β© 2014 Common Core, Inc. Some rights reserved. commoncore.org Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.