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!

4.5 in.

5 in. 4 in.

2 cm

4.6 cm3.5 cm

6 ft

6 ft

8 m

3 m

Find the area of the parallelogram with the given vertices!

P (1, 2)

Q (4, 2)

R (6, 5)

S (3, 5)

J (-3, -3)

K (0, 4)

L (5, 4)

M (2, -3)

13 in. 12 in.

10 in.

x

Find the value of x.

Just in case you were getting bored…

Find the height of the parallelogram!

15 cm

1.5 m

A = 600 cm2

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!

y

12

x30°

y

25 45°

x

Area of a Trapezoid:

Height

Recall: The height of a trapezoid is the ______________ distance between the bases.

Find each area. Don’t forget your units!

Leg Leg

Base1

Base2

12 m

20 m

10 m

10 in.

7 in.

4 in.

Find the area of each trapezoid!

6 m

6 m

12 m60°

6 m

4 ft 45°

ft26

ft28

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.

Area of a Kite or Rhombus:

Find each area.

Recall:

Kite: 2 pairs __________ sides , 0 pairs ___________ sides ||

Rhombus: ______ sides

d1

d2d1d2

A

B

CD

23

35

W X

YZ

5

512

12

45°10

27

Find the area of each kite or rhombus!

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.

a) Minor arc:

b) Major arc:

c) Semicircle:

d) Radius:

e) Diameter:

ZL

MNO

2rA

Area of a Circle!

Find the area of each circle. Leave answers in terms of π.

More Vocab:

• ________ of a circle:

• _________ of a circle:

region bounded by an arc and the two radii touching its endpoints

region bounded by an arc and the segment joining its endpoints

A

O

B

14 in. 10 in.12 in.

)(360

sectorofarea 2 rABarcofmeasure

AXB

Find the area of each sector. Leave answers in terms of π.

a) Sector CZD

b) Sector BZC

c) Sector BZA

ZA

DCB

72°

20 cm

Finding AREA of a sector!

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. 24 ft120°

More Areas!Find the area of the circle, sector BZD, and the shaded segment. Leave answers in terms of π.

ZA

DB

90°

6 m

Challenge Problems!Find the area of each shaded region. Leave answers in terms of π.

10 in. 15 cm

Did we meet the target?

Get started on the HW!

L.T.: Be able to find the area of circles, sectors, and segments of circles!!

Review:Find the value of each variable!

x

6

45°

y

x35

y

8

y

x60°

y

12

x30°

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:

• ______:

• ______:

• ________:

distance from the center to a vertex

perpendicular distance from the center to a side

center of the circle circumscribed about the regular polygon

Finding Angle Measures!

4

3

2

1

m

m

m

m

Find the measure of each numbered angle.

1

2

3

41

2

3

What would be the measure of each central angle in a nonagon?

In a 12-gon? In a 36-gon?

3

2

1

m

m

m

11

Finding Angle Measures!

3

2

1

m

m

m

Find the measure of each numbered angle.

23

2

3

3

2

1

m

m

m

Did we meet the target?

On your TICKET OUT, write the measure of each numbered angle!

L.T.: Be able to find measures of angles in polygons!

1 3

2

Review: Find the value of each variable!

x

6

45°

yy

12

x30°

1

2

3

41

2

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:

6 m

m33

ft16

ft38

cm4

cm2

Find the area of each regular polygon. Don’t forget your units!

Find the area of a regular heptagon with side length 5 cm and apothem 8 cm.

cm6.11

cm8cm8

cm316

ft6ft5

Find the area of each regular polygon. Don’t forget your units!

Find the area of a regular nonagon with side length 4.7 in. and apothem 6.5 in.

cm4

cm34 cm23

cm23

5 m

m35

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 cm.34

Warm-up: Find the value of each variable!

xx12

y30°

xy

1

2

3

3

2

1

m

m

m

Find the measures of each angle! Find the area!

m2

m34A

x

45°

5

5

Section 11.4 ~ day 3 Areas of Regular Polygons!!

L.T.: Be able to find the areas of regular polygons using special right triangles!

A

The next step:

Find the measure of each central angle, and then find the area of the regular hexagon!

centralm

Find the area of each regular polygon!A

ft25

AA

m310

in.12

Find the area of each regular polygon!

AA

ft16 cm4

A

m23

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. CELL1A

CELLS13A