GEOMETRY
NYS COMMON CORE MATHEMATICS CURRICULUM
Name _________________________
Lesson 10
M4
Date_____________
Lesson 10: Perimeter and Area of Polygonal Regions in the Plane
Learning Targets
 I can find the perimeter of a quadrilateral in the coordinate plane given its vertices and edges.

I can find the area of a quadrilateral in the coordinate plane given its vertices and edges
Opening Exercise (5 minutes)
Find the area of the triangle given using decomposition method
GEOMETRY
NYS COMMON CORE MATHEMATICS CURRICULUM
Name _________________________
Lesson 10
M4
Date_____________
Lesson 10: Perimeter and Area of Polygonal Regions in the Plane
Learning Targets
 I can find the perimeter of a quadrilateral in the coordinate plane given its vertices and edges.

I can find the area of a quadrilateral in the coordinate plane given its vertices and edges
Remember:
Example 1. Given the figure below, find the area by decomposing into rectangles and triangles.
Example 2.
a) Find the area of the trapezoid using the formula for the area of a trapezoid A=
b) Find the area using decomposing method
𝟏
𝟐
(𝒃𝟏 + 𝒃𝟐 ) ∙ 𝒉.
GEOMETRY
NYS COMMON CORE MATHEMATICS CURRICULUM
Name _________________________
Lesson 10
M4
Date_____________
Example 3. Find the area and perimeter of quadrilateral 𝑨𝑩𝑪𝑫
a) Perimeter:
b) Area using the decomposing method :
Example 4. Find the perimeter and the area of the quadrilateral with vertices 𝑨(−𝟑, 𝟒), 𝑩(𝟒, 𝟔), 𝑪(𝟐, −𝟑), and
𝑫(−𝟒, −𝟒).
a) Perimeter:
b) Area:
GEOMETRY
NYS COMMON CORE MATHEMATICS CURRICULUM
Name _________________________
Lesson 10
M4
Date_____________
Quick Check for Understanding
On your own:
1. The pentagon has vertices 𝐴(4, 7), 𝐵(2, 5), 𝐶(1, 2), 𝐷(3, 1), and 𝐸(5, 3). Calculate the area.
2. Find the perimeter of pentagon 𝑨𝑩𝑪𝑫𝑬 with vertices 𝑨(𝟐, 𝟔), 𝑩(𝟕, 𝟐), 𝑪(𝟑, −𝟒), 𝑫(−𝟑, −𝟐),
and 𝑬(−𝟐, 𝟒).
GEOMETRY
NYS COMMON CORE MATHEMATICS CURRICULUM
Name _________________________
Lesson 10
M4
Date_____________
Lesson 10: Perimeter and Area of Polygonal Regions in the Plane
Lesson 10 - Problem Set
1. * Given triangle 𝑨𝑩𝑪 and square 𝑫𝑬𝑭𝑮, find the area of each. Specify the method you chose to find the
area and why you chose that method (traditional or decomposing method).
2. *Find the area and perimeter of quadrilateral 𝑨𝑩𝑪𝑫 with vertices 𝑨(𝟔, 𝟓), 𝑩(𝟐, −𝟒), 𝑪(−𝟓, 𝟐),
and 𝑫(−𝟑, 𝟔).
GEOMETRY
Lesson 10
NYS COMMON CORE MATHEMATICS CURRICULUM
Name _________________________
M4
Date_____________
3. ** Find the area and perimeter of the hexagon shown.
4 ***. Katrina is making a scaled drawing for an L shaped garden on graph paper using the scale below. The
vertices of the L shape are as follows: (0,0) , (10,0), (10,2), (2,2). (2,6) and (0,6). Using the scale below, what is
the perimeter of the garden in feet?
1 space = 2 feet
(1) 28
(2) 32
(3) 56
(4) 64
GEOMETRY
NYS COMMON CORE MATHEMATICS CURRICULUM
Name _________________________
Lesson 10
M4
Date_____________
5***. The Terry Fencing Company has asked to give an estimate for the cost of enclosing a yard in the shape
of polygon ABCDE, with a privacy fence. The fence costs $9.95 per linear foot.
a.) Determine the amount of fencing to the nearest linear foot,
needed to enclose this property on all sides
b.) Using your answer from part a, what will the fencing project cost?