Understanding Area and Perimeter

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Understanding Area and Perimeter

• Amy Boesen
• CS255

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Perimeter

• Perimeter is simply the distance around an
  object.
• Everyday applications of perimeter include the
  distance around a fence or the distance around a
  pool.
• To figure out the perimeter of a rectangle,
  simply add up all the sides.

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Calculating Perimeter

• If the length of this rectangle is 10cm and it
  has a width of 4cm, what is the perimeter?

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Calculating Perimeter cont.

• There are two ways to figure this out. The first
  is to add all four sides.
• length length width width perimeter
• 10 10 4 4 28
• The second approach requires you to make an
  algebraic equation.
• 2(length) 2(width) perimeter
• 2(10) 2(4) 28

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Area

• Area usually deals with how much space an object
  covers or how much is needed to cover the object.
• Everyday applications of area include how much
  material it will take to cover a surface.

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Units

• The units for perimeter and area are not the
  same.
• For example If we make a dog pen that is 10
  feet long and 8 feet wide we would need 36 feet
  of fencing to surround the pen. However, if we
  were to calculate the area we would say that the
  pen covers 80 square feet.

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Calculating Area

• To calculate the area of a rectangle, simply
  multiply the length by the width.
• length x width area
• If a rectangle has a width of 6 feet and a
  length of 8 feet, what is the area?

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Calculating Area cont.

• To calculate the area of this rectangle, you
  would have this equation
• 6 feet x 8 feet 48 square feet
• Since you are multiplying feet x feet, your
  answer will be square feet. Area is always
  answered in square units.

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Perimeter of Triangles

• Finding the perimeter of a triangle is very
  similar to finding the perimeter of a rectangle.
  You simply add up the three sides.
• If a triangle has one side that is 22 cm long,
  another that is 17 cm, and a third that is 30 cm
  long, what is the perimeter?
• 22cm 17cm 30cm 69cm

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Area of Triangles

• Finding the area of a triangle is somewhat
  different than finding the area of a rectangle.
• With triangles we no longer can use length times
  width. We now use base times height. To keep it
  simple, we will stick to 90 degree triangles for
  now.
• The formula for the area of triangles is
• ½ x base x height

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Area of Triangles cont.

• The height of the triangle is the distance from
  the base to the point farthest away, measured
  along a perpendicular line.
• The height of this triangle is 4 inches and the
  base is 6 inches, what is its area?

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Area of Triangles cont.

• ½ x base x height area of triangle
• ½ x 6 inches x 4 inches 12 square inches

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Distance Around a Circle

• The distance around a circle is not called
  perimeter. It is called the circumference.
• To calculate the circumference of a circle we
  need to use pi. The value for pi is 3.14. Pi is
  the ratio of the circumference to the diameter of
  ANY circle.

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Circumference

• This gives us two possible formulas to calculate
  the circumference of a circle. One uses radius
  and the other uses diameter.
• circumference pi x diameter
• or
• circumference 2 x pi x radius

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Circumference cont.

• If the radius of a circle is 5 cm, what is the
  circumference?
• circumference pi x diameter
• c 3.14 x 10 c 31.4cm
• circumference 2 x pi x radius
• c 2 x 3.14 x 5 c 31.4

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Area of Circles

• The formula for the area of circles is a bit more
  complicated than the others.
• area pi x radius squared
• If a circle has a radius of 8 inches, what is
  its area?
• A 3.14 x 82
• A 200.96 square inches

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Summary

• We have learned many formulas for finding the
  perimeter and area of various objects such as
  rectangles, squares, triangles, and circles.
• We have learned that perimeter concerns how much
  is needed to surround an object and that area is
  how much is needed to cover an object.

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Summary cont.

• Lastly we learn that the relationship between
  area and perimeter is somewhat complicated. If
  you double the area of a square, you do not
  double its perimeter. However, two objects may
  have the same perimeters, but different areas or
  the same area, but different perimeters.
• You will understand this relationship more after
  some additional practice.