Area of Polygons

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Area of Polygons

• By Sara Gregurash

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Area

• The area of a polygon measures the size of the
  region that the figure occupies. It is
  2-dimensional like a table cloth. It is
  expressed in terms of some square unit. Some
  examples of the units used are square meters,
  square centimeters, square inches, or square
  kilometers.

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Area of a triangle

• To find the area of a triangle, you have to
  multiply the base by its height and divide by 2.
  You have to divide by two because a parallelogram
  can be divided into 2 triangles. The area of
  each triangle (2 of them) of a parallelogram is
  equal to one-half the area of the parallelogram.
  The equation is
• A ½ (bh)
• The b stands for the base of a triangle. The h
  stands for height. These are shown in the two
  diagrams below.

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Base and Height

• The base and height of a triangle have to be
  perpendicular. The base is a side of the
  triangle, but the height isnt always a side of
  the triangle. When you have a right triangle,
  then the height is the side of the triangle
  because it is perpendicular to the base. The
  sides of a triangle arent always perpendicular
  to the base. For example, when you have an obtuse
  triangle the side is slanted (this is shown
  below).

h 8 cm
b 4 cm
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Area of a right triangle

• Lets practice finding the area of triangles.
  The same formula is used to find the area of all
  triangles. I will show you how to find the area
  of right, acute, obtuse, scalene, and equilateral
  triangles. Here is an example using right
  triangles.
• For this triangle, the base is 6 cm and the
  height is 9 cm so you plug those numbers into the
  equation. It looks like this
• A ½ (2 in 4 in)
• A ½ (8 in2)
• A 4 in2

h 4 in
b 2 in
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Area of an acute and obtuse triangle

• The base of this acute triangle is 16 centimeters
  and the height is 7 centimeters.
• A ½ (16 cm 7 cm)
• A ½ (112 cm2)
• A 56 cm2
• The base of this obtuse triangle is 4 inches and
  the height is 8 inches.
• A ½ (8 in 4 in)
• A ½ (32 in2)
• A 16 in2

b 7 cm
b 16 cm
h 8 cm
b 4 cm
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Area of a scalene triangle

• A scalene triangle has all sides of different
  lengths.
• The base of this scalene triangle is 80
  millimeters and the height is 22 millimeters.
• A ½ (b h)
• A ½ (80 mm 22 mm)
• A ½ (1760 mm 2 )
• A 880 mm 2

b 80 mm
h 22 mm
s 50 mm
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Area of an equilateral triangle

• An equilateral triangle is a triangle with three
  equal length sides and the angles are all equal.
• To find the area of the equilateral triangle
  below with a side of 21 centimeters and the
  altitude is 14 centimeters, you have to use the
  formula.
• A ½ base or side altitude (height)
• A ½ (21 cm 14 cm)
• A ½ (294 cm 2 )
• A 147 cm 2

side (base) 21 cm
a 14 cm
Math Goodies Lesson is a good site to view to
practice your skills on area of triangles.
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Area of a square

• A square is a rectangle with 4 equal sides. To
  find the area of a square you multiply the
  distance along the side of the square by itself.
  The formula looks like this A s s (s is the
  distance along the side of the square)
• So, the length of each side of this square is 2
  inches.
• A 2 in 2 in
• A 4 in2

2 in
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Area of a rectangle

• A rectangle is a four-sided polygon that has
  opposite sides equal and are parallel. All four
  angles are right angles that are 90 degrees.
• To find the area of a rectangle you have to
  multiply the length by the width. The formula
  looks like this A L W (L is the length
  and W is the width of the rectangle)
• So, the length of this rectangle is 19
  centimeters and the width is 6 centimeters.
• A 19 cm 6 cm
• A 114 cm2

6 cm
19 cm
This sites has a lesson on area of squares and
rectangles.
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Parallelograms

• A parallelogram is a four-sided shape formed by
  two pairs of parallel lines. The opposite sides
  have the same length and the opposite angles have
  the same degree (size).
• To find the area of a parallelogram, you have to
  multiply its base by its height. The formula
  looks like this
• A b h (b is the base and h is the height)
• The base and height of a parallelogram must be
  perpendicular. The lateral sides of a
  parallelogram are not perpendicular to the base,
  so a dotted line is drawn to represent the
  height.

h
b
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Area of a parallelogram

• To find the area of this parallelogram, you
  multiply the base of 8 centimeters and the height
  of 3 centimeters.
• A b h
• A 8 cm 3 cm
• A 24 cm2

h 3 cm
b 8 cm
This site has a lesson about the area of
parallelograms.
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Trapezoids

• A trapezoid is a four-sided figure with one pair
  of parallel sides. The bases of the trapezoid
  below are parallel. To find the area of a
  trapezoid, you have to multiply the sum of its
  bases by the height and divided by 2. The
  formula looks like this
• A 1/2 (b1 b2) h ( b1 is base1, b2 is
  base2, and h is the height)
• Each base of a trapezoid must be perpendicular to
  the height. The lateral sides of the trapezoid
  arent perpendicular to either of the bases, so a
  dotted line is drawn to represent the height.

b1
h
b2
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Area of a trapezoid

• The trapezoid below has a b1 of 14 millimeters,
  b2 of 20 millimeters, and a height of 22
  millimeters. So, the area of this trapezoid is
• A 1/2 (b1 b2) h
• A 1/2 (14 mm 20 mm) 22 mm
• A 1/2 (34 mm) 22 mm
• A 1/2 748 mm2
• A 374 mm2

b1 14 mm
h 22 mm
b2 20 mm
This site has a lesson on the area of trapezoids.
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Practice Websites

• These sites have great examples of how to find
  the area of polygons and circles. The second one
  is a worksheet to help you practice your skills.
  It is a good idea to take a look at them and see
  if you learn more about area. Then you can take
  the quiz that it provides. After you do that,
  you can move on to my worksheet for more
  practice.
• Area of Polygons and Circles
• Worksheet on Area of Polygons and Circles

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Worksheet Time

• Now, that you have went through my lesson about
  areas of polygons. So, you can apply what you
  learned with this worksheet. Time to practice!
• Here are the answers to my worksheet.