write down objective and homework in agenda lay out homework (graphing picture) homework(area...
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WARM UP Write down objective and homework in
agenda Lay out homework (Graphing Picture) Homework(Area Review)
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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
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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
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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
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WHAT AREA FORMULAS CAN YOU REMEMBER? What do you remember about
perimeter?
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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.
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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
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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
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RECTANGLE
What is the perimeter of this rectangle?
l = 23 ft.
w = 6 ft.
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RECTANGLE
Perimeter = 2l + 2w = 2(23) + 2(6) = 46 + 12 = 58 ft.
l = 23 ft.
w = 6 ft.
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RECTANGLE
What is the area of this rectangle?
l = 23 ft.
w = 6 ft.
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RECTANGLE
l = 23 ft.
w = 6 ft.
Area = 23 x 6 = 138 sq. ft.
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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
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SQUARE
5.5 yds
What is the perimeter of this square?
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SQUARE
5.5 yds
Perimeter = 4s = 4(5.5) = 22.0 yds.
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SQUARE
5.5 yds
What is the area of this square?
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SQUARE
5.5 yds
Area = s 2= 5.5 2
= 30.25 sq. yds.
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PARALLELOGRAM
A parallelogram is a quadrilateral with oppositesides parallel. Opposite sides are also equal.
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PARALLELOGRAM
Area = (base)(height)
height
base
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PARALLELOGRAM
230 in.
150 in.
What is the perimeter of this parallelogram?
175 in.
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PARALLELOGRAM
230 in.
150 in.
Perimeter = 2b + 2s = 2(230) + 2(175) = 460 + 350 = 810 in.
175 in.
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PARALLELOGRAM
230 in.
150 in.
What is the area of this parallelogram?
175 in.
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PARALLELOGRAM
230 in.
150 in.
Area = 230 x 150 = 34,500 sq. in.
175 in.
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TRIANGLE
The perimeter of a triangle equals the sum of the lengths of its sides. Perimeter =s1 + s2 + s3
s1s2
s3
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TRIANGLE
Area = 1/2 (base)(height)
base
height
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TRIANGLE
5 ft
11.5 ft.
What is the perimeter of this triangle?
7 ft.9.5 ft.
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TRIANGLE
5 ft
11.5 ft.
7 ft.9.5 ft.
Perimeter = s1 + s2 + s3 = 11.5 + 7 + 9.5 = 28.0 ft.
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TRIANGLE
5 ft
11.5 ft.
What is the area of this triangle?
7 ft.9.5 ft.
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TRIANGLE
5 ft
11.5 ft.
Area = (1/2)(base)(height)= (1/2)(11.5)(5) = 28.75 sq. ft.
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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
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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)
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TRAPEZOID
What is the perimeter of this trapezoid?
18 in.
50 in.
20 in.
21 in.21 in.
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TRAPEZOID
18 in.
50 in.
20 in.
21 in.21 in.
Perimeter = B + b + s1 + s2 = 50 + 20 + 21 + 21 = 112 in.
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TRAPEZOID
18 in.
50 in.
20 in.
Area = (1/2)(h)(B + b) = (1/2)(18)(50 + 20) = 630 sq. in.
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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)!
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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.
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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
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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
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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
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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
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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
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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
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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
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6 inches
6 x 6 = 36 (area for the square)3.14 x 32 = 28.2636 – 28.26 = 7.74 inches
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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
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http://mathworld.wolfram.com/Circle.html
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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
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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
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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
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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
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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
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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