1.4 Perimeter and Area in the Coordinate Plane Question How can you find the perimeter and area of a quadrilateral in a coordinate plane? 1.4 Perimeter and Area in the Coordinate Plane

Geometry1.4 Perimeter and Area in the

Coordinate Plane

August 25, 20161.4 Perimeter and Area in the Coordinate Plane


1.4 Warm Up

Essential Question

How can you find the perimeter and area

of a quadrilateral in a coordinate plane?


What You Will Learn

• Classify polygons

• Find perimeters and areas of polygons in the

coordinate plane.



Polygons

• A plane figure made of three or more segments

(sides).

• Each side intersects exactly two other sides at their

endpoints.

• Polygons are named by vertices in consecutive

order, going CW or CCW.


These are Polygons


These are NOT polygons.

No

Segments/sides

Sides don’t

intersect at

endpoints.

Figure not

closed.

Naming Polygons

• The name tells you how many sides and how many

vertices the polygon has.

• Learn the names: memorize!

• Be able to spell them.



Triangle – 3 sides

A B

C

We say “Triangle ABC”

Vertex B


Quadrilateral – 4 sides

Q

R S

T

Name: QRST

We say “Quadrilateral QRST”


Pentagon – 5 sides

J

K L

M

NName: JKLMN


Hexagon – 6 sides

A

BC

D

E F

Name: FEDCBA


Heptagon – 7 sides


Octagon – 8 sides


Nonagon – 9 sides


Decagon – 10 sides


Names used on occasion

• undecagon – 11 sides (1 + 10 sides)

• dodecagon – 12 sides (2 + 10 sides)


More than 10 sides: n-gon

• 14-gon has 14 sides.




Convex & Concave

• All polygons are either convex or concave.

• It’s easy to determine which category falls in just

by looking.


Convex

• No extended sides are in the interior of the polygon.


Concave

• At least one extended side (or part of one) is in the

interior of the polygon.

Think: Caved In

Example 1

Classify each polygon by the number of sides. Tell

whether it is convex of concave.


a.

d.c.

b.

Quadrilateral,

Concave

Hexagon,

Convex

Heptagon,

Convex

Pentagon,

Concave

Perimeter and Area

Perimeter – The distance around a

figure.

Area – The square units it takes to

fill a figure.


Square


S

S

Perimeter

P = 4s

Area

A = s2

Rectangle


b

h

Perimeter

P = 2b + 2h

Area

A = bh

Parallelogram


Perimeter

P = add all sides

Area

A = bhb

h

Triangle


h

b

a c

Perimeter

P = add all sides

Area

bhA21

Example 2


Each side of a square measures 2.5 m. Find its

perimeter and its area.

2.5 m

2.5 m P = 4(2.5) = 10 m

A = 2.52 = 6.25 m2

Area is a

square

measure.

Example 3


3 in8 in

10 in

2 in

Find the perimeter and the area.

P = 3 + 10 + 8 = 21 in

A = ½ (10)(2) = 10 in2

Example 4


G(0, 1)

R(-2, -3) A(3,-3)

M(5, 1)

a. Find the perimeter of GRAM with vertices G(0, 1),

R(-2, -3), A(3, -3), and M(5, 1).

Example 4


G(0, 1)

R(-2, -3) A(3,-3)

M(5, 1)

b. Find the area of GRAM with vertices G(0, 1),

R(-2, -3), A(3, -3), and M(5, 1).

Example 5


You are building a shed in your backyard. The diagram shows the

four vertices of the shed. Each unit in the coordinate plane

represents 1 foot. Find the area of the floor of the shed.

Essential Question

How can you find the perimeter and area

of a quadrilateral in a coordinate plane?


Assignment


1.4 worksheet

Documents

1.4 Perimeter and Area in the Coordinate Plane Question How can you find the perimeter and area of a quadrilateral in a coordinate plane? 1.4 Perimeter and Area in the Coordinate Plane