Warm-up

1. List the properties that make a

quadrilateral a Parallelogram.

2. Find the area of the shaded region: (the radius is 12 – try ways to find the area of each)

•Opposite sides are congruent & parallel;

•Opposite angles are congruent;

•Consecutive angles are supplementary;

• Diagonals bisect each other

12²π – ½ 18(12√3) = 144π – 108√3)

~ 187.06 sq units

Find the right triangle!

Area Formulas

Write all the area formulas in your flip book!!

Kites

Parallelograms

Rectangles

)(2

121 bbhA

21*2

1ddA 21*

2

1ddA

hbA *

wlA *

2sA

Rhombi

Squares

Trapezoids

11.1 Areas of Triangles

and Parallelograms

Objective: Solve situations involving the area of polygons

Formulas

Area of a

Parallelogram

A = b * h

Area of a Triangle

A = ½ bh

Class Example: 1. Find the area of parallelogram RSTU.

R S

T U

20 in.

s 6 in.

45o

A = bh

A = 20(3)

A = 60in.2

1. What formula for the area of a parallelogram:

2. Figure out what you have and what you need:

What is the height?

3. Plug values into your formula!

A = bh

3

2. Find the area of parallelogram RSTU. R S

T U

15 in.

s 4 in.

30o

A = bh

A = 15(2)

A = 30 in.2

1. What formula

A = bh

2. Figure out what you have and what you need:

Since a 30-60-90

height = 2

3. Plug values into your formula!

4. Find the area.

4 in.

60o

h

h = 4√3 in.

A = ½ (4)(4√3)

A = 8√3 sq. in.

11.1 Activity

Find perimeter and area for odd each figure

11.2 Areas of Trapezoids,

Rhombuses, and Kites

Formulas:

Area of a Trapezoid: Area of a Rhombus: Area of a Kite:

)(2

121 bbhA

d1 d2

d1

d2

21*2

1ddA )(

2

121 bbhA

21*2

1ddA

Class Exercises:

2

21

42

14*62

1

*2

1

inA

A

ddA

2

21

28

)86(42

1

)(2

1

ftA

A

bbhA

2

21

2400

80*602

1

*2

1

mA

A

ddA

4. Find the height of a trapezoid that has an area of 287

square inches and bases of 38 inches and 44 inches.

hin

h

bbhA

.7

)4438(2

1287

)(2

121

38

44

h

3. Find the area of quadrilateral ABCD if

BE = 12, ED = 5, and AC = 20.

A E C

B

D

Area of ABCD = ½ (17)20 = 170

Area of quad. ABCD = 170 sq. units

What shape is it?

Quad with ┴ diagonals

What formula

A= ½ d1d2

5. A rhombus with a 20 centimeter diagonal has an area

of 300 square centimeters. Find the perimeter of

the rhombus.

2

2

2

21

30

10300

)20(2

1300

*2

1

d

d

d

ddA

x

x

x

x

x

135

13*25

325

225100

1510

2

2

222

10

10 15

15

x

cmP

P

1320

)135(4

x

x

x

xx

ddA

5.9

25.90

22

125.90

2*2

125.90

*2

1

2

2

21

Let d1=x and d2=2x.

So d1= x = 9.5 in. and d2= 2x = 2(9.5) = 19in.

Class Activity 2

Find the area of each odd

trapezoid and kite

Circles

Area of a circle =

Circumference =

2r2 r

Find the area of the

shaded region.

Geometry Homework:

Finish both activity sheets

and do

Working Backwards Worksheet