Areas of Parallelograms and Triangles!
L.T.#1: Be able to find the areas of parallelograms
(including rhombuses, rectangles, & squares)!
L.T.#2: Be able to find the areas of triangles!
Quick Review:
In a triangle, an altitude goes from a _______ and is
____________ to the opposite side.
Quick Vocab:
In a parallelogram, an altitude does the same thing!
This is also called the _______.
Area of any Parallelogram:
A
Area 

Note: The base can be any side—you choose! But, the height
depends on which side you pick to be the base.
Key: The base and height are always _____________ to each other.
Find the area of each parallelogram.
Don’t forget your units!
6 ft
4.5 in.
5 in.
4 in.
3m
8m
6 ft
4.6 cm
3.5 cm
2 cm
Find the area of the parallelogram with
the given vertices!
P (1, 2)
J (-3, -3)
Q (4, 2)
K (0, 4)
R (6, 5)
L (5, 4)
S (3, 5)
M (2, -3)
Just in case you were getting bored…
Find the height of the parallelogram!
15 cm
A = 600 cm2
1.5 m
Find the value of x.
x
13 in.
12 in.
10 in.
Section 11.2 ~ Areas of
Trapezoids, Rhombuses, and Kites!!
L.T.#1: Be able to find areas of trapezoids!
L.T.#2: Be able to find areas of rhombuses and kites!
Quick Review: Find the value of each variable!
12
y
30°
5 2
45°
x
y
x
Recall: The height of a trapezoid is the ______________
distance between the bases.
Area of a Trapezoid:
Base1
Leg
Leg
Height
Base2
Find each area. Don’t forget your units!
12 m
10 m
20 m
10 in.
4 in.
7 in.
Find the area of each trapezoid!
12 m
60°
6m
6m
6 2 ft
8 2 ft
6m
4 ft 45°
Are trapezoids in the real world?
The border of Arkansas resembles a trapezoid
with bases 190 mi and 250 mi, and height
242 mi. Approximate the area of Arkansas.
The border of car window resembles a trapezoid
with bases 20 in. and 36 in., and height 18 in.
Approximate the area of the window.
Recall:
Kite: 2 pairs __________ sides , 0 pairs ___________ sides ||
Rhombus: ______ sides 
Area of a Kite or Rhombus:
d1
d1
d2
d
2
Find each area.
B
A
3
X
5 12
3
2
D
W
5
12
C
Z
5
Y
Find the area of each kite or rhombus!
10
45°
7 2
15
12
Areas of Circles and Sectors!!
L.T.: Be able to find the area of circles, sectors, and
segments of circles!!
Quick Review:
Name the following from circle Z.
Z
L
a) Minor arc:
b) Major arc:
c) Semicircle:
d) Radius:
e) Diameter:
O
N
M
Area of a Circle!
A  r 
2
Find the area of each circle. Leave answers in terms of π.
14 in.
10 in.
12 in.
More Vocab:
• ________ of a circle: region bounded by an arc
and the two radii touching its endpoints
• _________ of a circle: region bounded by an
arc and the segment joining its endpoints
A
B
O
Finding AREA of a sector!
measure of arc AB
area of sector AXB 
 (r 2  )
360
Find the area of each sector. Leave answers in terms of π.
a) Sector CZD
b) Sector BZC
A
Z
20 cm
B
c) Sector BZA
D
C
72
°
Finding AREA of a segment!
1) Find the area of the sector.
2) Find the area of the triangle.
3) Subtract.
Find the area of each shaded region. Leave answers in terms of π.
10 in.
120°
24 ft
More Areas!
Find the area of the circle, sector BZD, and the shaded segment.
Leave answers in terms of π.
6m
A
Z
B
D
90°
Challenge Problems!
Find the area of each shaded region. Leave answers in terms of π.
10 in.
15 cm
Did we meet the target?
L.T.: Be able to find the area of circles, sectors, and
segments of circles!!
Get started on the HW!
Review:
Find the value of each variable!
5 3
6
x
x
45°
y
x
60°
y
8
12
30°
y
y
x
Section 11.4 ~ day 1
Areas of Regular Polygons!!
L.T.: Be able to find measures of angles in polygons!
Quick Review:
What is a “regular” polygon?
New Vocab:
center of the circle
• ______:
circumscribed about the
regular polygon
• ______: distance from the center to
a vertex
• ________: perpendicular distance
from the center to a side
Finding Angle Measures!
Find the measure of each numbered angle.
3
1
1
4
2
2
3
m1 
m1 
m2 
m2 
m3 
m3 
m4 
What would be the measure of each central angle in a nonagon?
In a 12-gon?
In a 36-gon?
Finding Angle Measures!
Find the measure of each numbered angle.
1
1
2
2
3
3
m1 
m1 
m2 
m3 
m2 
m3 
Did we meet the target?
L.T.: Be able to find measures of angles in polygons!
1
On your TICKET OUT, write the
measure of each numbered angle!
2
3
Review: Find the value of each variable!
12
6
30°
y
x
x
45°
y
1
1
4
2
2
3
3
Section 11.4 ~ day 2
Areas of Regular Polygons!!
L.T.: Be able to find the areas of regular polygons!
Area of any Regular Polygon:
3 3m
6m
8 3 ft
2 cm
4 cm
16 ft
Find the area of each regular polygon.
Don’t forget your units!
5 ft
6 ft
8 cm
8 cm
11.6 cm
16 3 cm
Find the area of a regular heptagon with side length
5 cm and apothem 8 cm.
Find the area of each regular polygon.
Don’t forget your units!
5 3m
5m
3 2 cm
4 cm
4 3 cm
3 2 cm
Find the area of a regular nonagon with side length
4.7 in. and apothem 6.5 in.
Did we meet the target?
L.T.: Be able to find the areas of regular polygons!
Find the area of a regular
hexagon with side length 8 cm
and apothem 4 3 cm.
Warm-up: Find the value of each variable!
y
x
30°
5
45°
x
x
12
5
y
Find the measures of each angle!
Find the area!
1
2
3
m1 
m2 
m3 
x
2m
4 3m
A
Section 11.4 ~ day 3
Areas of Regular Polygons!!
L.T.: Be able to find the areas of regular polygons using
special right triangles!
The next step:
Find the measure of each
central angle, and then find the
area of the regular hexagon!
m central  
A
Find the area of each regular polygon!
A
A
A
12 in.
5 2 ft
10 3 m
Find the area of each regular polygon!
A
A
3 2m
16 ft
A
4 cm
Thinking outside the box . . .
A regular hexagon has perimeter 120 m.
Find its area.
A
Un-bee-lievable!
Did you know that when bees
make honeycomb, each cell is a
regular hexagon? Since we are
craving some sweet honey, we
break off the piece of honeycomb
below. But before we extract the
honey, we think it would be pretty
SWEET to calculate the total area
of our honeycomb. We measure
that the radius of each cell is 1 cm.
A1 CELL 
A13 CELLS 