WARM UP Write down objective and homework in

agenda Lay out homework (Graphing Picture) Homework(Area Review)

WARM UP A square room with an area of 324

square feet is tiled using square tiles with a side length of 1 foot. How many tiles line each wall of the room?

A) 17 B) 18 C) 19 D) 20

VOCABULARY Area: number of square units that it takes to cover the

interior of a polygon, irregular figure, or circle Perimeter: distance measured around the sides of a

polygon , you find the perimeter by adding all sides together

area of a triangle: A=1/2 x b x h area of a rectangle: A= l x w area of a parallelogram: A = b x h area of a trapezoid: A = ½(b1+ b2)h Square: a parallelogram with four right angles and four

congruent sides Rectangle: a parallelogram with four right angles Parallelogram: a quadrilateral with both pairs of opposite

sides parallel Trapezoid: a quadrilateral with exactly one pair of parallel

sides Triangle: a polygon with three sides

VOCABULARY Rhombus: a parallelogram with four congruent

sides Circle: the set of all points in a plane that are

equidistant from a given point, called the center Chord: a segment whose endpoints are on the

circle Diameter: a chord that passes through the

center of the circle Radius: a segment that has one endpoint at the

center of the circle and the other endpoint on the circle

Circumference: the distance around a circle. You calculate the circumference of a circle by multiplying the diameter by π

WHAT AREA FORMULAS CAN YOU REMEMBER? What do you remember about

perimeter?

PERIMETER & AREA

The perimeter of a polygon is the distance around the outside of the polygon. It’s equal to the sum of the lengths of the sides of the polygon.

The area of a figure can be thought of as the space in the plane that the figure takes up.

RECTANGLE

To find the perimeter of a rectangle we need to know the length of its sides, l and w.Because opposite sides are equal we get the formula Perimeter = 2l + 2w

ww

l

l

RECTANGLE

To find the area of a rectangle see how many unit squares will fit in it.

The number of unit squares that will fit in the rectangle equals the area

of the rectangle. Notice that the total number of unit squares that will fit

in the rectangle equals the number of squares across times the number of

squares down. This leads us to Area = length x width

width

length

RECTANGLE

What is the perimeter of this rectangle?

l = 23 ft.

w = 6 ft.

RECTANGLE

Perimeter = 2l + 2w = 2(23) + 2(6) = 46 + 12 = 58 ft.

l = 23 ft.

w = 6 ft.

RECTANGLE

What is the area of this rectangle?

l = 23 ft.

w = 6 ft.

RECTANGLE

l = 23 ft.

w = 6 ft.

Area = 23 x 6 = 138 sq. ft.

SQUARE

A square is a special type of rectangle with length = width.If we call the length of a side s then

Perimeter = 4sArea = s2

SQUARE

5.5 yds

What is the perimeter of this square?

SQUARE

5.5 yds

Perimeter = 4s = 4(5.5) = 22.0 yds.

SQUARE

5.5 yds

What is the area of this square?

SQUARE

5.5 yds

Area = s 2= 5.5 2

= 30.25 sq. yds.

PARALLELOGRAM

A parallelogram is a quadrilateral with oppositesides parallel. Opposite sides are also equal.

PARALLELOGRAM

Area = (base)(height)

height

base

PARALLELOGRAM

230 in.

150 in.

What is the perimeter of this parallelogram?

175 in.

PARALLELOGRAM

230 in.

150 in.

Perimeter = 2b + 2s = 2(230) + 2(175) = 460 + 350 = 810 in.

175 in.

PARALLELOGRAM

230 in.

150 in.

What is the area of this parallelogram?

175 in.

PARALLELOGRAM

230 in.

150 in.

Area = 230 x 150 = 34,500 sq. in.

175 in.

TRIANGLE

The perimeter of a triangle equals the sum of the lengths of its sides. Perimeter =s1 + s2 + s3

s1s2

s3

TRIANGLE

Area = 1/2 (base)(height)

base

height

TRIANGLE

5 ft

11.5 ft.

What is the perimeter of this triangle?

7 ft.9.5 ft.

TRIANGLE

5 ft

11.5 ft.

7 ft.9.5 ft.

Perimeter = s1 + s2 + s3 = 11.5 + 7 + 9.5 = 28.0 ft.

TRIANGLE

5 ft

11.5 ft.

What is the area of this triangle?

7 ft.9.5 ft.

TRIANGLE

5 ft

11.5 ft.

Area = (1/2)(base)(height)= (1/2)(11.5)(5) = 28.75 sq. ft.

TRAPEZOID

A trapezoid is a quadrilateral with 2 sides parallel. The two parallel sides are called the bases and are labeled B and b.

B

b

TRAPEZOID

B

b

hh

The area of the trapezoid is the sum of the areas of the two triangles.Area = (1/2)(B)(h) + (1/2)(b)(h)

Factoring (1/2)(h) out of each term we getArea = (1/2)(h)(B + b)

TRAPEZOID

What is the perimeter of this trapezoid?

18 in.

50 in.

20 in.

21 in.21 in.

TRAPEZOID

18 in.

50 in.

20 in.

21 in.21 in.

Perimeter = B + b + s1 + s2 = 50 + 20 + 21 + 21 = 112 in.

TRAPEZOID

18 in.

50 in.

20 in.

Area = (1/2)(h)(B + b) = (1/2)(18)(50 + 20) = 630 sq. in.

THE VALUE OF Π

For any circle the circumference is always just over three times bigger than the diamter.

The exact number is called π (pi).

We use the symbol π because the number cannot be written exactly.

π = 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196 (to 200 decimal places)!

APPROXIMATIONS FOR THE VALUE OF Π

When we are doing calculations involving the value π we have to use an approximation for the value.

Generally, we use the approximation 3.14

We can also use the π button on a calculator.

When a calculation has lots of steps we write π as a symbol throughout and evaluate it at the end, if necessary.

THE CIRCUMFERENCE OF A CIRCLE

For any circle,

π =circumference

diameter

or,

We can rearrange this to make a formula to find the circumference of a circle given its diameter.

C = πd

π =C

d

THE CIRCUMFERENCE OF A CIRCLE

Use π = 3.14 to find the circumference of this circle.

C = πd8 cm

= 3.14 × 8

= 25.12 cm

FIND THE PERIMETER OF THIS SHAPE

Use π = 3.14 to find perimeter of this shape.

The perimeter of this shape is made up of the circumference of a circle of diameter 13 cm and two lines of length 6 cm.

6 cm13 cm

Perimeter = 3.14 × 13 + 6 + 6

= 52.82 cm

FORMULA FOR THE AREA OF A CIRCLE

We can find the area of a circle using the formula

radius

Area of a circle = πr2

Area of a circle = π × r × r

or

THE AREA OF A CIRCLE

Use π = 3.14 to find the area of this circle.

A = πr24 cm

= 3.14 × 4 × 4

= 50.24 cm2

THE AREA OF A CIRCLE

Use π = 3.14 to find the area of the following circles:

A = πr22 cm

= 3.14 × 22

= 12.56 cm2

A = πr2

10 m= 3.14 × 52

= 78.5 m2

A = πr2

23 mm= 3.14 × 232

= 1661.06 mm2

A = πr2

78 cm= 3.14 × 392

= 4775.94 cm2

FIND THE AREA OF THIS SHAPE

Use π = 3.14 to find area of this shape.

The area of this shape is made up of the area of a circle of diameter 13 cm and the area of a rectangle of width 6 cm and length 13 cm.

6 cm13 cm Area of circle = 3.14 × 6.52

= 132.665 cm2

Area of rectangle = 6 × 13

= 78 cm2

Total area = 132.665 + 78

= 210.665 cm2

6 inches

6 x 6 = 36 (area for the square)3.14 x 32 = 28.2636 – 28.26 = 7.74 inches

REVIEW OF AREA! http://www.regentsprep.org/Regents/mat

h/ALGEBRA/AS1/PracArea.htm http://www.ixl.com/math/geometry/area-

and-perimeter-mixed-review

http://mathworld.wolfram.com/Circle.html

SQUAREThe square frame around the clock on Big Ben is a 7 meter square. What are the perimeter and area of the frame around the clock on the tower?

P = 2L + 2WP = 28 metersA = lwA = 49 meters

RECTANGLE

Central Park in New York City is 2.5 miles long and 0.5 miles wide. What are the perimeter and area of Central Park?

P = 2L + 2WP = 6 milesA = lwA= 1.25 miles

TRIANGLEThe Louvre in Paris has a pyramid that serves as the main entrance. Each face of the pyramid is 35 meters long and has a height of about 27.03 meters. What is the area of each face?

A = 1/2bhA = 473.025

PARALLELOGRAMThis building stands at the foot of Mt. Yatsugatake in Japan. It was designed to be an architect’s studio. If the base is about 6 meters long and 23.4 meters tall, what is the area of the face of the house facing you in this photograph?A = 140.4 meters

RHOMBUSThe windows of the Swiss Re building in London are rhombi. Each side length of the rhombi are approximately 5.7 ft. long. Given this length, what would be the perimeter of each rhombus?P=22.8 feet

TRAPEZOIDEye Bank is a medical facility in Venice, Italy. The trapezoid walls stand 12 meters high. The ground piece of the trapezoid is approximately 24 meters long and the top of the trapezoids are approximately 30 meters long. Given these dimensions, find the area of each trapezoid.A = 324 meters