Lesson 10
NYS COMMON CORE MATHEMATICS CURRICULUM
M4
GEOMETRY
Lesson 10: Perimeter and Area of Polygonal Regions in the
Cartesian Plane
Classwork
Opening Exercise
Find the area of the triangle given. Compare your answer and method to your neighbor’s and discuss differences.
Lesson 10:
Date:
Perimeter and Area of Polygonal Regions in the Cartesian Plane
8/27/14
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
S.41
Lesson 10
NYS COMMON CORE MATHEMATICS CURRICULUM
M4
GEOMETRY
Exercises 1–6
1.
Given rectangle
:
a.
Identify the vertices.
b.
Find the perimeter using the distance formula.
c.
Find the area using the area formula.
d.
List the vertices starting with
e.
Verify the area using the shoelace formula.
Lesson 10:
Date:
moving counterclockwise.
Perimeter and Area of Polygonal Regions in the Cartesian Plane
8/27/14
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
S.42
Lesson 10
NYS COMMON CORE MATHEMATICS CURRICULUM
M4
GEOMETRY
2.
Calculate the area and perimeter of the given quadrilateral using the shoelace formula.
3.
Break up the pentagon to find the area using Green’s theorem. Compare your method with a partner.
Lesson 10:
Date:
Perimeter and Area of Polygonal Regions in the Cartesian Plane
8/27/14
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
S.43
Lesson 10
NYS COMMON CORE MATHEMATICS CURRICULUM
M4
GEOMETRY
4.
Find the perimeter and the area of the quadrilateral with vertices
5.
Find the area of the pentagon with vertices
Lesson 10:
Date:
and
and
.
.
Perimeter and Area of Polygonal Regions in the Cartesian Plane
8/27/14
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
S.44
Lesson 10
NYS COMMON CORE MATHEMATICS CURRICULUM
M4
GEOMETRY
6.
Find the area and perimeter of the hexagon shown.
Lesson 10:
Date:
Perimeter and Area of Polygonal Regions in the Cartesian Plane
8/27/14
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
S.45
Lesson 10
NYS COMMON CORE MATHEMATICS CURRICULUM
M4
GEOMETRY
Problem Set
1.
2.
Given triangle
with vertices
,
, and
:
a.
Calculate the perimeter using the distance formula.
b.
Calculate the area using the traditional area formula.
c.
Calculate the area using the shoelace formula.
d.
Explain why the shoelace formula might be more useful and efficient if you were just asked to find the area.
Given triangle
and quadrilateral
describe how you would find the area of each and why you would
choose that method, and then find the areas.
Lesson 10:
Date:
Perimeter and Area of Polygonal Regions in the Cartesian Plane
8/27/14
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
S.46
Lesson 10
NYS COMMON CORE MATHEMATICS CURRICULUM
M4
GEOMETRY
3.
Find the area and perimeter of quadrilateral
4.
Find the area and perimeter of pentagon
Lesson 10:
Date:
with vertices
and
with vertices
and
Perimeter and Area of Polygonal Regions in the Cartesian Plane
8/27/14
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
S.47
Lesson 10
NYS COMMON CORE MATHEMATICS CURRICULUM
M4
GEOMETRY
5.
Show that the shoelace formula (Green’s theorem) used on the trapezoid shown confirms the traditional formula for
the area of a trapezoid
Lesson 10:
Date:
Perimeter and Area of Polygonal Regions in the Cartesian Plane
8/27/14
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
S.48